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qcp.m
function qcp() % Copyright 2024, Gurobi Optimization, LLC % % 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) % x, y, z non-negative 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 using a sparse matrix model.quadcon(1).Qc = sparse([ 1 0 0; 0 1 0; 0 0 -1]); model.quadcon(1).q = zeros(3,1); model.quadcon(1).rhs = 0.0; model.quadcon(1).name = 'std_cone'; % Add rotated cone: x^2 <= yz using sparse triplet representation % Equivalent sparse matrix data: %model.quadcon(2).Qc = sparse([ % 1 0 0; % 0 0 -1; % 0 0 0]); model.quadcon(2).Qrow = [1, 2] model.quadcon(2).Qcol = [1, 3] model.quadcon(2).Qval = [1, -1] % All-zero sparse 3-by-1 vector model.quadcon(2).q = sparse(3,1); model.quadcon(2).rhs = 0.0; model.quadcon(2).name = 'rot_cone'; 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); end