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### qp.m

function qp()
% Copyright 2019, 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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