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# R API - Common Arguments

Most common arguments in the Gurobi R interface are R `list` variables, each containing multiple `named components`. Several of these named components are optional. Note that you refer to a named component of a list variable by adding a dollar sign to the end of the variable name, followed by the name of the named component. For example, `model$A` refers to named component `A` of variable `model`.

## The model argument

Model variables store optimization problems (as described in the problem statement).

Models can be built in a number of ways. You can populate the appropriate named components of the `model` list using standard R routines. You can also read a model from a file, using `gurobi_read`. A few API functions (`gurobi_feasrelax` and `gurobi_relax`) also return models.

Note that all matrix named components within the `model` variable can be dense or sparse. Sparse matrices should be built using either `sparseMatrix` from the `Matrix` package, or `simple_triplet_matrix` from the `slam` package.

The following is an enumeration of all of the named components of the `model` argument that Gurobi will take into account when optimizing the model:

### Commonly used named components

A

  The linear constraint matrix.

obj (optional)

  The linear objective vector (the `c` vector in the problem statement). When present, you must specify one value for each column of `A`. When absent, each variable has a default objective coefficient of 0.

sense (optional)

  The senses of the linear constraints. Allowed values are `=`, `<`, or `>`. You must specify one value for each row of `A`, or a single value to specify that all constraints have the same sense. When absent, all senses default to `<`.

rhs (optional)

  The right-hand side vector for the linear constraints (\(b\) in the problem statement). You must specify one value for each row of `A`. When absent, the right-hand side vector defaults to the zero vector.

lb (optional)

  The lower bound vector. When present, you must specify one value for each column of `A`. When absent, each variable has a default lower bound of 0.

ub (optional)

  The upper bound vector. When present, you must specify one value for each column of `A`. When absent, the variables have infinite upper bounds.

vtype (optional)

  The variable types. This vector is used to capture variable integrality constraints. Allowed values are `C` (continuous), `B` (binary), `I` (integer), `S` (semi-continuous), or `N` (semi-integer). Binary variables must be either 0 or 1. Integer variables can take any integer value between the specified lower and upper bounds. Semi-continuous variables can take any value between the specified lower and upper bounds, or a value of zero. Semi-integer variables can take any integer value between the specified lower and upper bounds, or a value of zero. When present, you must specify one value for each column of `A`, or a single value to specify that all variables have the same type. When absent, each variable is treated as being continuous. Refer to the variable section of the reference manual for more information on variable types.

modelsense (optional)

  The optimization sense. Allowed values are `min` (minimize) or `max` (maximize). When absent, the default optimization sense is minimization.

modelname (optional)

  The name of the model. The name appears in the Gurobi log, and when writing a model to a file.

objcon (optional)

  The constant offset in the objective function (\(\mathrm{alpha}\) in the problem statement).

varnames (optional)

  The variable names vector. A character vector. When present, each element of this vector defines the name of a variable. You must specify a name for each column of `A`.

constrnames (optional)

  The constraint names vector. A character vector. When present, each element of the vector defines the name of a constraint. You must specify a name for each row of `A`.

### Quadratic objective and constraint named components

Q (optional)

  The quadratic objective matrix. When present, `Q` must be a square matrix whose row and column counts are equal to the number of columns in `A`.

quadcon (optional)

  The quadratic constraints. A list of lists. When present, each element in `quadcon` defines a single quadratic constraint: \(x^TQc\, x + q^Tx \le \mathrm{beta}\).

  The `Qc` matrix must be a square matrix whose row and column counts are equal to the number of columns of `A`. It is stored in `model$quadcon[[i]]$Qc`.

  The optional `q` vector defines the linear terms in the constraint. It can be a dense vector specifying a value for each column of `A` or a sparse vector (should be built using `sparseVector` from the `Matrix` package). It is stored in `model$quadcon[[i]]$q`.

  The scalar `beta` is stored in `model$quadcon[[i]]$rhs`. It defines the right-hand side value for the constraint.

  The optional `sense` string defines the sense of the quadratic constraint. Allowed values are `<`, `=` or `>`. If not present, the default sense is `<`. It is stored in `model$quadcon[[i]]$sense`.

  The optional `name` string defines the name of the quadratic constraint. It is stored in `model$quadcon[[i]]$name`.

### SOS constraint named components

sos (optional)

  The Special Ordered Set (SOS) constraints. A list of lists. When present, each entry in `sos` defines a single SOS constraint. A SOS constraint can be of type 1 or 2. The type of SOS constraint \(i\) is specified via `model$sos[[i]]$type`. A type 1 SOS constraint is a set of variables where at most one variable in the set may take a value other than zero. A type 2 SOS constraint is an ordered set of variables where at most two variables in the set may take non-zero values. If two take non-zeros values, they must be contiguous in the ordered set. The members of an SOS constraint are specified by placing their indices in vector `model$sos[[i]]$index`. Weights associated with SOS members are provided in vector `model$sos[[i]]$weight`. Please refer to SOS Constraints section in the reference manual for details on SOS constraints.

### Multi-objective named components

multiobj (optional)

  Multi-objective specification for the model. A list of lists. When present, each entry in `multiobj` defines a single objective of a multi-objective problem. Please refer to the Multiple Objectives section in the reference manual for more details on multi-objective optimization. Each objective \(i\) may have the following named components:

  objn

    Specified via `model$multiobj[[i]]$objn`. This is the i-th objective vector.

  objcon (optional)

    Specified via `model$multiobj[[i]]$objcon`. If provided, this is the i-th objective constant. The default value is 0.

  priority (optional)

    Specified via `model$multiobj[[i]]$priority`. If provided, this value is the hierarchical priority for this objective. The default value is 0.

  weight (optional)

    Specified via `model$multiobj[[i]]$weight`. If provided, this value is the multiplier used when aggregating objectives. The default value is 1.0.

  reltol (optional)

    Specified via `model$multiobj[[i]]$reltol`. If provided, this value specifies the relative objective degradation when doing hierarchical multi-objective optimization. The default value is 0.

  abstol (optional)

    Specified via `model$multiobj[[i]]$abstol`. If provided, this value specifies the absolute objective degradation when doing hierarchical multi-objective optimization. The default value is 0.

  name (optional)

    Specified via `model$multiobj[[i]]$name`. If provided, this string specifies the name of the i-th objective function.

  Note that when multiple objectives are present, the `result$objval` named component that is returned in the result of an optimization call will be a vector of the same length as `model$multiobj`.

  A multi-objective model can’t have other objectives. Thus, combining `model$multiobj` with any of `model$obj`, `model$objcon`, `model$pwlobj`, or `model$Q` is an error.

### Computing an IIS

When computing an Irreducible Inconsistent Subsystem (IIS) for an infeasible model, additional model attributes for variable bounds, linear constraints, quadratic constraints and general constraints may be set in order to indicate whether the corresponding entity should be explicitly included or excluded from the IIS:

iislbforce (optional)

  list of length equal to the number of variables. The value of `model$iislbforce[[i]]` specifies the IIS force attribute for the lower bound of the \(i\)-th variable.

iisubforce (optional)

  list of length equal to the number of variables. The value of `model$iisubforce[[i]]` specifies the IIS force attribute for the upper bound of the \(i\)-th variable.

iisconstrforce (optional)

  list of length equal to the number of constraints. The value of `model$iisconstrforce[[i]]` specifies the IIS force attribute for the \(i\)-th constraint.

iisqconstrforce (optional)

  list of length equal to the number of quadratic constraints. The value of `model$iisqconstrforce[[i]]` specifies the IIS force attribute for the \(i\)-th quadratic constraint.

iisgenconstrforce (optional)

  list of length equal to the number of general constraints. The value of `model$iisgenconstrforce[[i]]` specifies the IIS force attribute for the \(i\)-th general constraint.

Possible values for all five attribute of listsfrom above are: \(-1\) to let the algorithm decide, \(0\) to exclude the corresponding entity from the IIS, and \(1\) to always include the corresponding entity in the IIS.

Note that setting this attribute to 0 may make the resulting subsystem feasible (or consistent), which would then make it impossible to construct an IIS. Trying anyway will result in a IIS_NOT_INFEASIBLE error. Similarly, setting this attribute to 1 may result in an IIS that is not irreducible. More precisely, the system would only be irreducible with respect to the model elements that have force values of -1 or 0.

### General constraint named components

The list of lists described below are used to add general constraints to a model. Please refer to the General Constraints section in the reference manual for additional details on general constraints.

genconmax (optional)

  A list of lists. When present, each entry in `genconmax` defines a MAX general constraint of the form

  \[x[\mathrm{resvar}] = \max\left\{\mathrm{con},x[j]:j\in\mathrm{vars}\right\}\]

  Each entry may have the following named components:

  resvar

    Specified via `model$genconmax[[i]]$resvar`. Index of the variable in the left-hand side of the constraint.

  vars

    Specified via `model$genconmax[[i]]$vars`, it is a vector of indices of variables in the right-hand side of the constraint.

  con (optional)

    Specified via `model$genconmax[[i]]$con`. When present, specifies the constant on the left-hand side. Default value is \(-\infty\).

  name (optional)

    Specified via `model$genconmax[[i]]$name`. When present, specifies the name of the \(i\)-th MAX general constraint.

genconmin (optional)

  A list of lists. When present, each entry in `genconmax` defines a MIN general constraint of the form

  \[x[\mathrm{resvar}] = \min\left\{\mathrm{con},x[j]:j\in\mathrm{vars}\right\}\]

  Each entry may have the following named components:

  resvar

    Specified via `model$genconmin[[i]]$resvar`. Index of the variable in the left-hand side of the constraint.

  vars

    Specified via `model$genconmin[[i]]$vars`, it is a vector of indices of variables in the right-hand side of the constraint.

  con (optional)

    Specified via `model$genconmin[[i]]$con`. When present, specifies the constant on the left-hand side. Default value is \(\infty\).

  name (optional)

    Specified via `model$genconmin[[i]]$name`. When present, specifies the name of the \(i\)-th MIN general constraint.

genconabs (optional)

  A list of lists. When present, each entry in `genconmax` defines an ABS general constraint of the form

  \[x[\mathrm{resvar}] = \vert x[\mathrm{argvar}]\vert\]

  Each entry may have the following named components:

  resvar

    Specified via `model$genconabs[[i]]$resvar`. Index of the variable in the left-hand side of the constraint.

  argvar

    Specified via `model$genconabs[[i]]$argvar`. Index of the variable in the right-hand side of the constraint.

  name (optional)

    Specified via `model$genconabs[[i]]$name`. When present, specifies the name of the \(i\)-th ABS general constraint.

genconand (optional)

  A list of lists. When present, each entry in `genconand` defines an AND general constraint of the form

  \[x[\mathrm{resvar}] = \mathrm{and}\{x[i]:i\in\mathrm{vars}\}\]

  Each entry may have the following named components:

  resvar

    Specified via `model$genconand[[i]]$resvar`. Index of the variable in the left-hand side of the constraint.

  vars

    Specified via `model$genconand[[i]]$vars`, it is a vector of indices of variables in the right-hand side of the constraint.

  name (optional)

    Specified via `model$genconand[[i]]$name`. When present, specifies the name of the \(i\)-th AND general constraint.

genconor (optional)

  A list of lists. When present, each entry in `genconor` defines an OR general constraint of the form

  \[x[\mathrm{resvar}] = \mathrm{or}\{x[i]:i\in\mathrm{vars}\}\]

  Each entry may have the following named components:

  resvar

    Specified via `model$genconor[[i]]$resvar`. Index of the variable in the left-hand side of the constraint.

  vars

    Specified via `model$genconor[[i]]$vars`, it is a vector of indices of variables in the right-hand side of the constraint.

  name (optional)

    Specified via `model$genconor[[i]]$name`. When present, specifies the name of the \(i\)-th OR general constraint.

genconnorm (optional)

  A list of lists. When present, each entry in `genconnorm` defines a NORM general constraint of the form

  \[x[\mathrm{resvar}] = \mathrm{norm}(x[i]:i\in\mathrm{vars}, \mathrm{which})\]

  Each entry may have the following named components:

  resvar

    Specified via `model$genconnorm[[i]]$resvar`. Index of the variable in the left-hand side of the constraint.

  vars

    Specified via `model$genconnorm[[i]]$vars`, it is a vector of indices of variables in the right-hand side of the constraint.

  which

    Specified via `model$genconnorm[[i]]$which`. Specifies which p-norm to use. Possible values are 0, 1, 2 and \(\infty\).

  name (optional)

    Specified via `model$genconnorm[[i]]$name`. When present, specifies the name of the \(i\)-th NORM general constraint.

genconind (optional)

  A list of lists. When present, each entry in `genconind` defines an INDICATOR general constraint of the form

  \[x[\mathrm{binvar}] = \mathrm{binval}\Rightarrow\sum\left( x[j]\cdot\mathrm{a}[j]\right) \ \mathrm{sense} \ \mathrm{rhs}\]

  This constraint states that when the binary variable \(x[\mathrm{binvar}]\) takes the value `binval` then the linear constraint \(\sum\left(x[\mathrm{vars}[j]]\cdot\mathrm{val}[j]\right) \ \mathrm{sense} \ \mathrm{rhs}\) must hold. Note that `sense` is one of `=`, `<`, or `>` for equality (\(=\)), less than or equal (\(\leq\)) or greater than or equal (\(\geq\)) constraints. Each entry may have the following named components:

  binvar

    Specified via `model$genconind[[i]]$binvar`. Index of the implicating binary variable.

  binval

    Specified via `model$genconind[[i]]$binval`. Value for the binary variable that forces the following linear constraint to be satisfied. It can be either 0 or 1.

  a

    Specified via `model$genconind[[i]]$a`. Vector of coefficients of variables participating in the implied linear constraint. You can specify a value for `a` for each column of `A` (dense vector) or pass a sparse vector (should be built using `sparseVector` from the `Matrix` package).

  sense

    Specified via `model$genconind[[i]]$sense`. Sense of the implied linear constraint. Must be one of `=`, `<`, or `>`.

  rhs

    Specified via `model$genconind[[i]]$rhs`. Right-hand side value of the implied linear constraint.

  name (optional)

    Specified via `model$genconind[[i]]$name`. When present, specifies the name of the \(i\)-th INDICATOR general constraint.

genconpwl (optional)

  A list of lists. When present, each entry in `genconpwl` defines a piecewise-linear constraint of the form

  \[x[\mathrm{yvar}] = f(x[\mathrm{xvar}])\]

  The breakpoints for \(f\) are provided as arguments. Refer to the description of piecewise-linear objectives for details of how piecewise-linear functions are defined

  Each entry may have the following named components:

  xvar

    Specified via `model$genconpwl[[i]]$xvar`. Index of the variable in the right-hand side of the constraint.

  yvar

    Specified via `model$genconpwl[[i]]$yvar`. Index of the variable in the left-hand side of the constraint.

  xpts

    Specified via `model$genconpwl[[i]]$xpts`. Specifies the \(x\) values for the points that define the piecewise-linear function. Must be in non-decreasing order.

  ypts

    Specified via `model$genconpwl[[i]]$ypts`. Specifies the \(y\) values for the points that define the piecewise-linear function.

  name (optional)

    Specified via `model$genconpwl[[i]]$name`. When present, specifies the name of the \(i\)-th piecewise-linear general constraint.

genconpoly (optional)

  Deprecated since version 13.0: Using function constraints is deprecated since version 13.0. Please use nonlinear constraints instead.

  A list of lists. When present, each entry in `genconpoly` defines a polynomial function constraint of the form

  \[x[\mathrm{yvar}] = p_0 x[\mathrm{xvar}]^d + p_1 x[\mathrm{xvar}]^{d-1} + ... + p_{d-1} x[\mathrm{xvar}] + p_{d}\]

  A piecewise-linear approximation of the function is added to the model. The details of the approximation are controlled using the following four attributes (or using the parameters with the same names): FuncPieces, FuncPieceError, FuncPieceLength, and FuncPieceRatio. Alternatively, the function can be treated as a nonlinear constraint by setting the attribute FuncNonlinear. For details, consult the General Constraint discussion.

  Each entry may have the following named components:

  xvar

    Specified via `model$genconpoly[[i]]$xvar`. Index of the variable in the right-hand side of the constraint.

  yvar

    Specified via `model$genconpoly[[i]]$yvar`. Index of the variable in the left-hand side of the constraint.

  p

    Specified via `model$genconpoly[[i]]$p`. Specifies the coefficients for the polynomial function (starting with the coefficient for the highest power). If \(x^d\) is the highest power term, a dense vector of length \(d+1\) is returned.

  name (optional)

    Specified via `model$genconpoly[[i]]$name`. When present, specifies the name of the \(i\)-th polynomial function constraint.

  funcpieces (optional)

    Specified via `model$genconpoly[[i]]$funcpieces`. When present, specifies the FuncPieces attribute of the \(i\)-th polynomial function constraint.

  funcpiecelength (optional)

    Specified via `model$genconpoly[[i]]$funcpiecelength`. When present, specifies the FuncPieceLength attribute of the \(i\)-th polynomial function constraint.

  funcpieceerror (optional)

    Specified via `model$genconpoly[[i]]$funcpieceerror`. When present, specifies the FuncPieceError attribute of the \(i\)-th polynomial function constraint.

  funcpieceratio (optional)

    Specified via `model$genconpoly[[i]]$funcpieceratio`. When present, specifies the FuncPieceRatio attribute of the \(i\)-th polynomial function constraint.

  funcnonlinear (optional)

    Specified via `model$genconpoly[[i]]$funcnonlinear`. When present, specifies the FuncNonlinear attribute of the \(i\)-th polynomial function constraint.

genconexp (optional)

  Deprecated since version 13.0: Using function constraints is deprecated since version 13.0. Please use nonlinear constraints instead.

  A list of lists. When present, each entry in `genconexp` defines the natural exponential function constraint of the form

  \[x[\mathrm{yvar}] = \mathrm{exp}(x[\mathrm{xvar}])\]

  A piecewise-linear approximation of the function is added to the model. The details of the approximation are controlled using the following four attributes (or using the parameters with the same names): FuncPieces, FuncPieceError, FuncPieceLength, and FuncPieceRatio. Alternatively, the function can be treated as a nonlinear constraint by setting the attribute FuncNonlinear. For details, consult the General Constraint discussion.

  Each entry may have the following named components:

  xvar

    Specified via `model$genconexp[[i]]$xvar`. Index of the variable in the right-hand side of the constraint.

  yvar

    Specified via `model$genconexp[[i]]$yvar`. Index of the variable in the left-hand side of the constraint.

  name (optional)

    Specified via `model$genconexp[[i]]$name`. When present, specifies the name of the \(i\)-th natural exponential function constraint.

  funcpieces (optional)

    Specified via `model$genconexp[[i]]$funcpieces`. When present, specifies the FuncPieces attribute of the \(i\)-th natural exponential function constraint.

  funcpiecelength (optional)

    Specified via `model$genconexp[[i]]$funcpiecelength`. When present, specifies the FuncPieceLength attribute of the \(i\)-th natural exponential function constraint.

  funcpieceerror (optional)

    Specified via `model$genconexp[[i]]$funcpieceerror`. When present, specifies the FuncPieceError attribute of the \(i\)-th natural exponential function constraint.

  funcpieceratio (optional)

    Specified via `model$genconexp[[i]]$funcpieceratio`. When present, specifies the FuncPieceRatio attribute of the \(i\)-th natural exponential function constraint.

  funcnonlinear (optional)

    Specified via `model$genconexp[[i]]$funcnonlinear`. When present, specifies the FuncNonlinear attribute of the \(i\)-th natural exponential function constraint.

genconexpa (optional)

  Deprecated since version 13.0: Using function constraints is deprecated since version 13.0. Please use nonlinear constraints instead.

  A list of lists. When present, each entry in `genconexpa` defines an exponential function constraint of the form

  \[x[\mathrm{yvar}] = \mathrm{a}^{x[\mathrm{xvar}]}\]

  A piecewise-linear approximation of the function is added to the model. The details of the approximation are controlled using the following four attributes (or using the parameters with the same names): FuncPieces, FuncPieceError, FuncPieceLength, and FuncPieceRatio. Alternatively, the function can be treated as a nonlinear constraint by setting the attribute FuncNonlinear. For details, consult the General Constraint discussion.

  Each entry may have the following named components:

  xvar

    Specified via `model$genconexpa[[i]]$xvar`. Index of the variable in the right-hand side of the constraint.

  yvar

    Specified via `model$genconexpa[[i]]$yvar`. Index of the variable in the left-hand side of the constraint.

  a

    Specified via `model$genconexpa[[i]]$a`. Specifies the base of the exponential function \(a > 0\).

  name (optional)

    Specified via `model$genconexpa[[i]]$name`. When present, specifies the name of the \(i\)-th exponential function constraint.

  funcpieces (optional)

    Specified via `model$genconexpa[[i]]$funcpieces`. When present, specifies the FuncPieces attribute of the \(i\)-th exponential function constraint.

  funcpiecelength (optional)

    Specified via `model$genconexpa[[i]]$funcpiecelength`. When present, specifies the FuncPieceLength attribute of the \(i\)-th exponential function constraint.

  funcpieceerror (optional)

    Specified via `model$genconexpa[[i]]$funcpieceerror`. When present, specifies the FuncPieceError attribute of the \(i\)-th exponential function constraint.

  funcpieceratio (optional)

    Specified via `model$genconexpa[[i]]$funcpieceratio`. When present, specifies the FuncPieceRatio attribute of the \(i\)-th exponential function constraint.

  funcnonlinear (optional)

    Specified via `model$genconexpa[[i]]$funcnonlinear`. When present, specifies the FuncNonlinear attribute of the \(i\)-th exponential function constraint.

genconlog (optional)

  Deprecated since version 13.0: Using function constraints is deprecated since version 13.0. Please use nonlinear constraints instead.

  A list of lists. When present, each entry in `genconlog` defines the natural logarithmic function constraint of the form

  \[x[\mathrm{yvar}] = \mathrm{log}(x[\mathrm{xvar}])\]

  A piecewise-linear approximation of the function is added to the model. The details of the approximation are controlled using the following four attributes (or using the parameters with the same names): FuncPieces, FuncPieceError, FuncPieceLength, and FuncPieceRatio. Alternatively, the function can be treated as a nonlinear constraint by setting the attribute FuncNonlinear. For details, consult the General Constraint discussion.

  Each entry may have the following named components:

  xvar

    Specified via `model$genconlog[[i]]$xvar`. Index of the variable in the right-hand side of the constraint.

  yvar

    Specified via `model$genconlog[[i]]$yvar`. Index of the variable in the left-hand side of the constraint.

  name (optional)

    Specified via `model$genconlog[[i]]$name`. When present, specifies the name of the \(i\)-th natural logarithmic function constraint.

  funcpieces (optional)

    Specified via `model$genconlog[[i]]$funcpieces`. When present, specifies the FuncPieces attribute of the \(i\)-th natural logarithmic function constraint.

  funcpiecelength (optional)

    Specified via `model$genconlog[[i]]$funcpiecelength`. When present, specifies the FuncPieceLength attribute of the \(i\)-th natural logarithmic function constraint.

  funcpieceerror (optional)

    Specified via `model$genconlog[[i]]$funcpieceerror`. When present, specifies the FuncPieceError attribute of the \(i\)-th natural logarithmic function constraint.

  funcpieceratio (optional)

    Specified via `model$genconlog[[i]]$funcpieceratio`. When present, specifies the FuncPieceRatio attribute of the \(i\)-th natural logarithmic function constraint.

  funcnonlinear (optional)

    Specified via `model$genconlog[[i]]$funcnonlinear`. When present, specifies the FuncNonlinear attribute of the \(i\)-th natural logarithmic function constraint.

genconloga (optional)

  Deprecated since version 13.0: Using function constraints is deprecated since version 13.0. Please use nonlinear constraints instead.

  A list of lists. When present, each entry in `genconloga` defines a logarithmic function constraint of the form

  \[x[\mathrm{yvar}] = \mathrm{log}(x[\mathrm{xvar}])\setminus\mathrm{log}(a)\]

  A piecewise-linear approximation of the function is added to the model. The details of the approximation are controlled using the following four attributes (or using the parameters with the same names): FuncPieces, FuncPieceError, FuncPieceLength, and FuncPieceRatio. Alternatively, the function can be treated as a nonlinear constraint by setting the attribute FuncNonlinear. For details, consult the General Constraint discussion.

  Each entry may have the following named components:

  xvar

    Specified via `model$genconloga[[i]]$xvar`. Index of the variable in the right-hand side of the constraint.

  yvar

    Specified via `model$genconloga[[i]]$yvar`. Index of the variable in the left-hand side of the constraint.

  a

    Specified via `model$genconloga[[i]]$a`. Specifies the base of the logarithmic function \(a > 0\).

  name (optional)

    Specified via `model$genconloga[[i]]$name`. When present, specifies the name of the \(i\)-th logarithmic function constraint.

  funcpieces (optional)

    Specified via `model$genconloga[[i]]$funcpieces`. When present, specifies the FuncPieces attribute of the \(i\)-th logarithmic function constraint.

  funcpiecelength (optional)

    Specified via `model$genconloga[[i]]$funcpiecelength`. When present, specifies the FuncPieceLength attribute of the \(i\)-th logarithmic function constraint.

  funcpieceerror (optional)

    Specified via `model$genconloga[[i]]$funcpieceerror`. When present, specifies the FuncPieceError attribute of the \(i\)-th logarithmic function constraint.

  funcpieceratio (optional)

    Specified via `model$genconloga[[i]]$funcpieceratio`. When present, specifies the FuncPieceRatio attribute of the \(i\)-th logarithmic function constraint.

  funcnonlinear (optional)

    Specified via `model$genconloga[[i]]$funcnonlinear`. When present, specifies the FuncNonlinear attribute of the \(i\)-th logarithmic function constraint.

genconlogistic (optional)

  Deprecated since version 13.0: Using function constraints is deprecated since version 13.0. Please use nonlinear constraints instead.

  A list of lists. When present, each entry in `genconlog` defines the logistic function constraint of the form

  \[x[\mathrm{yvar}] = 1 / (1 + \mathrm{exp}(-x[\mathrm{xvar}]))\]

  A piecewise-linear approximation of the function is added to the model. The details of the approximation are controlled using the following four attributes (or using the parameters with the same names): FuncPieces, FuncPieceError, FuncPieceLength, and FuncPieceRatio. Alternatively, the function can be treated as a nonlinear constraint by setting the attribute FuncNonlinear. For details, consult the General Constraint discussion.

  Each entry may have the following named components:

  xvar

    Specified via `model$genconlogistic[[i]]$xvar`. Index of the variable in the right-hand side of the constraint.

  yvar

    Specified via `model$genconlogistic[[i]]$yvar`. Index of the variable in the left-hand side of the constraint.

  name (optional)

    Specified via `model$genconlogistic[[i]]$name`. When present, specifies the name of the \(i\)-th logistic function constraint.

  funcpieces (optional)

    Specified via `model$genconlogistic[[i]]$funcpieces`. When present, specifies the FuncPieces attribute of the \(i\)-th logistic function constraint.

  funcpiecelength (optional)

    Specified via `model$genconlogistic[[i]]$funcpiecelength`. When present, specifies the FuncPieceLength attribute of the \(i\)-th logistic function constraint.

  funcpieceerror (optional)

    Specified via `model$genconlogistic[[i]]$funcpieceerror`. When present, specifies the FuncPieceError attribute of the \(i\)-th logistic function constraint.

  funcpieceratio (optional)

    Specified via `model$genconlogistic[[i]]$funcpieceratio`. When present, specifies the FuncPieceRatio attribute of the \(i\)-th logistic function constraint.

  funcnonlinear (optional)

    Specified via `model$genconlogistic[[i]]$funcnonlinear`. When present, specifies the FuncNonlinear attribute of the \(i\)-th logistic function constraint.

genconpow (optional)

  Deprecated since version 13.0: Using function constraints is deprecated since version 13.0. Please use nonlinear constraints instead.

  A list of lists. When present, each entry in `genconpow` defines a power function constraint of the form

  \[x[\mathrm{yvar}] = x[\mathrm{xvar}]^\mathrm{a}\]

  A piecewise-linear approximation of the function is added to the model. The details of the approximation are controlled using the following four attributes (or using the parameters with the same names): FuncPieces, FuncPieceError, FuncPieceLength, and FuncPieceRatio. Alternatively, the function can be treated as a nonlinear constraint by setting the attribute FuncNonlinear. For details, consult the General Constraint discussion.

  Each entry may have the following named components:

  xvar

    Specified via `model$genconpow[[i]]$xvar`. Index of the variable in the right-hand side of the constraint.

  yvar

    Specified via `model$genconpow[[i]]$yvar`. Index of the variable in the left-hand side of the constraint.

  a

    Specified via `model$genconpow[[i]]$a`. Specifies the exponent of the power function.

  name (optional)

    Specified via `model$genconpow[[i]]$name`. When present, specifies the name of the \(i\)-th power function constraint.

  funcpieces (optional)

    Specified via `model$genconpow[[i]]$funcpieces`. When present, specifies the FuncPieces attribute of the \(i\)-th power function constraint.

  funcpiecelength (optional)

    Specified via `model$genconpow[[i]]$funcpiecelength`. When present, specifies the FuncPieceLength attribute of the \(i\)-th power function constraint.

  funcpieceerror (optional)

    Specified via `model$genconpow[[i]]$funcpieceerror`. When present, specifies the FuncPieceError attribute of the \(i\)-th power function constraint.

  funcpieceratio (optional)

    Specified via `model$genconpow[[i]]$funcpieceratio`. When present, specifies the FuncPieceRatio attribute of the \(i\)-th power function constraint.

  funcnonlinear (optional)

    Specified via `model$genconpow[[i]]$funcnonlinear`. When present, specifies the FuncNonlinear attribute of the \(i\)-th power function constraint.

genconsin (optional)

  Deprecated since version 13.0: Using function constraints is deprecated since version 13.0. Please use nonlinear constraints instead.

  A list of lists. When present, each entry in `genconsin` defines the sine function constraint of the form

  \[x[\mathrm{yvar}] = \mathrm{sin}(x[\mathrm{xvar}])\]

  A piecewise-linear approximation of the function is added to the model. The details of the approximation are controlled using the following four attributes (or using the parameters with the same names): FuncPieces, FuncPieceError, FuncPieceLength, and FuncPieceRatio. Alternatively, the function can be treated as a nonlinear constraint by setting the attribute FuncNonlinear. For details, consult the General Constraint discussion.

  Each entry may have the following named components:

  xvar

    Specified via `model$genconsin[[i]]$xvar`. Index of the variable in the right-hand side of the constraint.

  yvar

    Specified via `model$genconsin[[i]]$yvar`. Index of the variable in the left-hand side of the constraint.

  name (optional)

    Specified via `model$genconsin[[i]]$name`. When present, specifies the name of the \(i\)-th sine function constraint.

  funcpieces (optional)

    Specified via `model$genconsin[[i]]$funcpieces`. When present, specifies the FuncPieces attribute of the \(i\)-th sine function constraint.

  funcpiecelength (optional)

    Specified via `model$genconsin[[i]]$funcpiecelength`. When present, specifies the FuncPieceLength attribute of the \(i\)-th sine function constraint.

  funcpieceerror (optional)

    Specified via `model$genconsin[[i]]$funcpieceerror`. When present, specifies the FuncPieceError attribute of the \(i\)-th sine function constraint.

  funcpieceratio (optional)

    Specified via `model$genconsin[[i]]$funcpieceratio`. When present, specifies the FuncPieceRatio attribute of the \(i\)-th sine function constraint.

  funcnonlinear (optional)

    Specified via `model$genconsin[[i]]$funcnonlinear`. When present, specifies the FuncNonlinear attribute of the \(i\)-th sine function constraint.

genconcos (optional)

  Deprecated since version 13.0: Using function constraints is deprecated since version 13.0. Please use nonlinear constraints instead.

  A list of lists. When present, each entry in `genconcos` defines the cosine function constraint of the form

  \[x[\mathrm{yvar}] = \mathrm{cos}(x[\mathrm{xvar}])\]

  A piecewise-linear approximation of the function is added to the model. The details of the approximation are controlled using the following four attributes (or using the parameters with the same names): FuncPieces, FuncPieceError, FuncPieceLength, and FuncPieceRatio. Alternatively, the function can be treated as a nonlinear constraint by setting the attribute FuncNonlinear. For details, consult the General Constraint discussion.

  Each entry may have the following named components:

  xvar

    Specified via `model$genconcos[[i]]$xvar`. Index of the variable in the right-hand side of the constraint.

  yvar

    Specified via `model$genconcos[[i]]$yvar`. Index of the variable in the left-hand side of the constraint.

  name (optional)

    Specified via `model$genconcos[[i]]$name`. When present, specifies the name of the \(i\)-th cosine function constraint.

  funcpieces (optional)

    Specified via `model$genconcos[[i]]$funcpieces`. When present, specifies the FuncPieces attribute of the \(i\)-th cosine function constraint.

  funcpiecelength (optional)

    Specified via `model$genconcos[[i]]$funcpiecelength`. When present, specifies the FuncPieceLength attribute of the \(i\)-th cosine function constraint.

  funcpieceerror (optional)

    Specified via `model$genconcos[[i]]$funcpieceerror`. When present, specifies the FuncPieceError attribute of the \(i\)-th cosine function constraint.

  funcpieceratio (optional)

    Specified via `model$genconcos[[i]]$funcpieceratio`. When present, specifies the FuncPieceRatio attribute of the \(i\)-th cosine function constraint.

  funcnonlinear (optional)

    Specified via `model$genconcos[[i]]$funcnonlinear`. When present, specifies the FuncNonlinear attribute of the \(i\)-th cosine function constraint.

gencontan (optional)

  Deprecated since version 13.0: Using function constraints is deprecated since version 13.0. Please use nonlinear constraints instead.

  A list of lists. When present, each entry in `gencontan` defines the tangent function constraint of the form

  \[x[\mathrm{yvar}] = \mathrm{tan}(x[\mathrm{xvar}])\]

  A piecewise-linear approximation of the function is added to the model. The details of the approximation are controlled using the following four attributes (or using the parameters with the same names): FuncPieces, FuncPieceError, FuncPieceLength, and FuncPieceRatio. Alternatively, the function can be treated as a nonlinear constraint by setting the attribute FuncNonlinear. For details, consult the General Constraint discussion.

  Each entry may have the following named components:

  xvar

    Specified via `model$gencontan[[i]]$xvar`. Index of the variable in the right-hand side of the constraint.

  yvar

    Specified via `model$gencontan[[i]]$yvar`. Index of the variable in the left-hand side of the constraint.

  name (optional)

    Specified via `model$gencontan[[i]]$name`. When present, specifies the name of the \(i\)-th tangent function constraint.

  funcpieces (optional)

    Specified via `model$gencontan[[i]]$funcpieces`. When present, specifies the FuncPieces attribute of the \(i\)-th tangent function constraint.

  funcpiecelength (optional)

    Specified via `model$gencontan[[i]]$funcpiecelength`. When present, specifies the FuncPieceLength attribute of the \(i\)-th tangent function constraint.

  funcpieceerror (optional)

    Specified via `model$gencontan[[i]]$funcpieceerror`. When present, specifies the FuncPieceError attribute of the \(i\)-th tangent function constraint.

  funcpieceratio (optional)

    Specified via `model$gencontan[[i]]$funcpieceratio`. When present, specifies the FuncPieceRatio attribute of the \(i\)-th tangent function constraint.

  funcnonlinear (optional)

    Specified via `model$gencontan[[i]]$funcnonlinear`. When present, specifies the FuncNonlinear attribute of the \(i\)-th tangent function constraint.

### Advanced named components

pwlobj (optional)

  The piecewise-linear objective functions. A list of lists. When present, each entry in `pwlobj` defines a piecewise-linear objective function for a single variable. The index of the variable whose objective function is being defined is stored in `model$pwlobj[[i]]$var`. The \(x\) values for the points that define the piecewise-linear function are stored in `model$pwlobj[[i]]$x`. The values in the \(x\) vector must be in non-decreasing order. The \(y\) values for the points that define the piecewise-linear function are stored in `model$pwlobj[[i]]$y`.

vbasis (optional)

  The variable basis status vector. Used to provide an advanced starting point for the simplex algorithm. You would generally never concern yourself with the contents of this vector, but would instead simply pass it from the result of a previous optimization run to the input of a subsequent run. When present, you must specify one value for each column of `A`.

cbasis (optional)

  The constraint basis status vector. Used to provide an advanced starting point for the simplex algorithm. Consult the `vbasis` description for details. When present, you must specify one value for each row of `A`.

varhintval (optional)

  A set of user hints. If you know that a variable is likely to take a particular value in high quality solutions of a MIP model, you can provide that value as a hint. You can also (optionally) provide information about your level of confidence in a hint with the `varhintpri` named component. If present, you must specify one value for each column of `A`. Use a value of `NA` for variables where no such hint is known. For more details, please refer to the Attribute section in the reference manual.

varhintpri (optional)

  Priorities on user hints. After providing variable hints through the `varhintval` list, you can optionally also provide hint priorities to give an indication of your level of confidence in your hints. If present, you must specify a value for each column of `A`. For more details, please refer to the Attribute section in the reference manual.

branchpriority (optional)

  Variable branching priority. If present, the value of this attribute is used as the primary criteria for selecting a fractional variable for branching during the MIP search. Variables with larger values always take priority over those with smaller values. Ties are broken using the standard branch variable selection criteria. If present, you must specify one value for each column of `A`.

pstart (optional)

  The current simplex start vector. If you set `pstart` values for every variable in the model and `dstart` values for every constraint, then simplex will use those values to compute a warm start basis. For more details, please refer to the Attribute section in the reference manual.

dstart (optional)

  The current simplex start vector. If you set `dstart` values for every linear constraint in the model and `pstart` values for every variable, then simplex will use those values to compute a warm start basis. For more details, please refer to the Attribute section in the reference manual.

lazy (optional)

  Determines whether a linear constraint is treated as a lazy constraint. If present, you must specify one value for each row of `A`. For more details, please refer to the Attribute section in the reference manual.

start (optional)

  The MIP start vector. The MIP solver will attempt to build an initial solution from this vector. When present, you must specify a start value for each variable. Note that you can set the start value for a variable to `NA`, which instructs the MIP solver to try to fill in a value for that variable.

partition (optional)

  The MIP variable partition number, which is used by the MIP solution improvement heuristic. If present, you must specify one value for each variable of `A`. For more details, please refer to the Attribute section in the reference manual.

If any of the mandatory components listed above are missing, the `gurobi()` function will return an error.

Below is an example that demonstrates the construction of a simple optimization model:

    model <- list()
    model$A <- matrix(c(1,2,3,1,1,0), nrow=2, byrow=T)
    model$obj <- c(1,1,1)
    model$modelsense <- 'max'
    model$rhs <- c(4,1)
    model$sense <- c('<', '>')

You can also build `A` as a sparse matrix, using either `sparseMatrix` or `simple_triplet_matrix`:

    model$A <- spMatrix(2, 3, c(1, 1, 1, 2, 2), c(1, 2, 3, 1, 2),  c(1, 2, 3, 1, 1))

    model$A <- simple_triplet_matrix(c(1, 1, 1, 2, 2), c(1, 2, 3, 1, 2), c(1, 2, 3, 1, 1))

Note that the Gurobi R interface allows you to specify a scalar value for most of the array-valued components. The specified value will be expanded to an array of the appropriate size, with each component of the array equal to the scalar (e.g., `model$obj <- 1` would be equivalent to `model$obj <- c(1,1,1)` in the example).

## The params argument

As mentioned previously, the Gurobi Optimizer provides a set of parameters that allow you to control many of the details of the optimization process. Factors like feasibility and optimality tolerances, choices of algorithms, strategies for exploring the MIP search tree, etc., can be controlled by modifying Gurobi parameters before beginning the optimization.

Parameter changes are specified using a `list` variable having multiple `named components`, which is passed as an argument to the appropriate Gurobi function (e.g., `gurobi`). The name of each named component must be the name of a Gurobi parameter, and the associated value should be the desired value of that parameter. You can find a complete list of the available Gurobi parameters in the reference manual.

To create a list that would set the Gurobi Method parameter to 2 and the ResultFile parameter to `model.mps`, you would do the following:

    params params$Method <- 2
    params$ResultFile <- 'model.mps'

We should say a bit more about the ResultFile parameter. If this parameter is set, the optimization model that is eventually passed to Gurobi will also be output to the specified file. The filename suffix should be one of `.mps`, `.rew`, `.lp`, `.rlp`, `.dua`, `.dlp`, `.ilp`, or `.opb`, to indicate the desired file format (see the file format section in the reference manual for details on Gurobi file formats).

The params struct can also be used to set license specific parameters, that define the computational environment to be used. We will discuss the two most common use cases next, and refer again to the collection of all available parameters in the reference manual.

### Using a Compute Server License

Gurobi Compute Server allows you to offload optimization jobs to a remote server. Servers are organized into clusters. By providing the name of any node within the cluster, your job will automatically be sent to the least heavily loaded node in the cluster. If all nodes are at capacity, your job will be placed in a queue, and will proceed once capacity becomes available. You can find additional information about Gurobi Compute Server in the Gurobi Remote Services Reference Manual. The most commonly used parameters are the following.

ComputeServer

  A Compute Server. You can refer to the server using its name or its IP address. If you are using a non-default port, the server name should be followed by the port number (e.g., `server1:61000`).

ServerPassword (optional)

  User password on the Compute Server cluster. Obtain this from your Compute Server administrator.

CSPriority (optional)

  The priority of the job. Priorities must be between -100 and 100, with a default value of 0 (by convention). Higher priority jobs are chosen from the server job queue before lower priority jobs. A job with priority 100 runs immediately, bypassing the job queue and ignoring the job limit on the server. You should exercise caution with priority 100 jobs, since they can severely overload a server, which can cause jobs to fail, and in extreme cases can cause the server to crash.

CSRouter (optional)

  The router for the Compute Server cluster. A router can be used to improve the robustness of a Compute Server deployment. You can refer to the router using either its name or its IP address. A typical Remote Services deployment won’t use a router, so you typically won’t need to set this.

CSTLSinsecure (optional)

  Indicates whether to use insecure mode in the TLS (Transport Layer Security). Leave this at its default value of 0 unless your server administrator tells you otherwise.

Here is an example of how to use a `params` argument to connect to a Compute Server:

    params params$ComputeServer <- 'server1.mycompany.com:61000'
    params$CSPriority <- 5

### Using a Gurobi Instant Cloud License

Gurobi Instant Cloud allows you to offload optimization jobs to a Gurobi Compute Server on the cloud. If an appropriate machine is already running, the job will run on that machine. It will automatically launch a new machine otherwise. Note that launching a new machine can take a few minutes. You can find additional information about the Gurobi Instant Cloud service in the reference manual. The most commonly used parameters are the following.

CloudAccessID

  The access ID for your Gurobi Instant Cloud license. This can be retrieved from the Gurobi Instant Cloud website. When used in combination with your CloudSecretKey, this allows you to launch Instant Cloud instances and submit jobs to them.

CloudSecretKey

  The secret key for your Gurobi Instant Cloud license. This can be retrieved from the Gurobi Instant Cloud website. When used in combination with your CloudAccessID, this allows you to launch Instant Cloud instances and submit jobs to them. Note that you should keep your secret key private.

CloudPool (optional)

  The machine pool. Machine pools allow you to create fixed configurations on the Instant Cloud website (capturing things like type of machine, geographic region, etc.), and then launch and share machines from client programs without having to restate configuration information each time you launch a machine. If not provided, your job will be launched in the default pool associated with your cloud license.

CSPriority (optional)

  The priority of the job. Priorities must be between -100 and 100, with a default value of 0 (by convention). Higher priority jobs are chosen from the server job queue before lower priority jobs. A job with priority 100 runs immediately, bypassing the job queue and ignoring the job limit on the server. You should exercise caution with priority 100 jobs, since they can severely overload a server, which can cause jobs to fail, and in extreme cases can cause the server to crash.

Here is an example of how to use a `params` argument to launch a Gurobi Instant Cloud instance:

    params params$CloudAccessID <- '3d1ecef9-dfad-eff4-b3fa'
    params$CloudSecretKey <- 'ae6L23alJe3+fas'

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