dense.py

#!/usr/bin/env python3.11

# Copyright 2025, Gurobi Optimization, LLC

# This example formulates and solves the following simple QP model:
#
#    minimize    x + y + x^2 + x*y + y^2 + y*z + z^2
#    subject to  x + 2 y + 3 z >= 4
#                x +   y       >= 1
#                x, y, z non-negative
#
# The example illustrates the use of dense matrices to store A and Q
# (and dense vectors for the other relevant data).  We don't recommend
# that you use dense matrices, but this example may be helpful if you
# already have your data in this format.

import sys
import gurobipy as gp
from gurobipy import GRB


def dense_optimize(rows, cols, c, Q, A, sense, rhs, lb, ub, vtype, solution):
    model = gp.Model()

    # Add variables to model
    vars = []
    for j in range(cols):
        vars.append(model.addVar(lb=lb[j], ub=ub[j], vtype=vtype[j]))

    # Populate A matrix
    for i in range(rows):
        expr = gp.LinExpr()
        for j in range(cols):
            if A[i][j] != 0:
                expr += A[i][j] * vars[j]
        model.addLConstr(expr, sense[i], rhs[i])

    # Populate objective
    obj = gp.QuadExpr()
    for i in range(cols):
        for j in range(cols):
            if Q[i][j] != 0:
                obj += Q[i][j] * vars[i] * vars[j]
    for j in range(cols):
        if c[j] != 0:
            obj += c[j] * vars[j]
    model.setObjective(obj)

    # Solve
    model.optimize()

    # Write model to a file
    model.write("dense.lp")

    if model.status == GRB.OPTIMAL:
        x = model.getAttr("X", vars)
        for i in range(cols):
            solution[i] = x[i]
        return True
    else:
        return False


# Put model data into dense matrices

c = [1, 1, 0]
Q = [[1, 1, 0], [0, 1, 1], [0, 0, 1]]
A = [[1, 2, 3], [1, 1, 0]]
sense = [GRB.GREATER_EQUAL, GRB.GREATER_EQUAL]
rhs = [4, 1]
lb = [0, 0, 0]
ub = [GRB.INFINITY, GRB.INFINITY, GRB.INFINITY]
vtype = [GRB.CONTINUOUS, GRB.CONTINUOUS, GRB.CONTINUOUS]
sol = [0] * 3

# Optimize

success = dense_optimize(2, 3, c, Q, A, sense, rhs, lb, ub, vtype, sol)

if success:
    print(f"x: {sol[0]:g}, y: {sol[1]:g}, z: {sol[2]:g}")