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### qcp.m

% Copyright 2016, Gurobi Optimization, Inc.

% This example formulates and solves the following simple QCP model:
%  maximize
%      x
%  subject to
%      x + y + z = 1
%      x^2 + y^2 <= z^2 (second-order cone)
%      x^2 <= yz        (rotated second-order cone)

clear model
names = {'x', 'y', 'z'};
model.varnames = names;

% Set objective: x
model.obj = [ 1 0 0 ];
model.modelsense = 'max';

% Add constraint: x + y + z = 1
model.A   = sparse([1 1 1]);
model.rhs = 1;
model.sense = '=';

% Add second-order cone: x^2 + y^2 <= z^2
model.quadcon(1).Qc = sparse([ 1 0  0;
0 1  0;
0 0 -1]);

% Add rotated cone: x^2 <= yz
model.quadcon(2).Qc = sparse([ 1 0  0;
0 0 -1;
0 0  0]);

gurobi_write(model, 'qcp.lp');

result = gurobi(model);

for j=1:3
fprintf('%s %e\n', names{j}, result.x(j))
end

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


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