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# qp.m

    function qp()
    % Copyright 2025, Gurobi Optimization, LLC
    %
    % This example formulates and solves the following simple QP model:
    %  minimize
    %      x^2 + x*y + y^2 + y*z + z^2 + 2 x
    %  subject to
    %      x + 2 y + 3 z >= 4
    %      x +   y       >= 1
    %      x, y, z non-negative
    %
    % It solves it once as a continuous model, and once as an integer
    % model.

    names = {'x', 'y', 'z'};
    model.varnames = names;
    model.Q = sparse([1 0.5 0; 0.5 1 0.5; 0 0.5 1]);
    model.A = sparse([1 2 3; 1 1 0]);
    model.obj = [2 0 0];
    model.rhs = [4 1];
    model.sense = '>';

    gurobi_write(model, 'qp.lp');

    results = gurobi(model);

    for v=1:length(names)
        fprintf('%s %e\n', names{v}, results.x(v));
    end

    fprintf('Obj: %e\n', results.objval);

    model.vtype = 'B';

    results  = gurobi(model);

    for v=1:length(names)
        fprintf('%s %e\n', names{v}, results.x(v));
    end

    fprintf('Obj: %e\n', results.objval);

    end

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