Bilinear.m

函数Bilinear％该示例制定并解决以下简单的双线性模型：％最大化x％对X + Y + Z <= 10％x * Y <= 2（双线性不等式）％x * z + y * z = 1（bilinear equality) % x, y, z non-negative (x integral in second version) % Copyright 2021, Gurobi Optimization, LLC % Linear constraint matrix m.A = sparse([1, 1, 1]); m.sense = '<'; m.rhs = 10; % Variable names m.varnames = {'x', 'y', 'z'}; % Objective function max 1.0 * x m.obj = [1; 0; 0]; m.modelsense = 'max'; % Bilinear inequality constraint: x * y <= 2 m.quadcon(1).Qrow = 1; m.quadcon(1).Qcol = 2; m.quadcon(1).Qval = 1.0; m.quadcon(1).q = sparse(3,1); m.quadcon(1).rhs = 2.0; m.quadcon(1).sense = '<'; m.quadcon(1).name = 'bilinear0'; % Bilinear equality constraint: x * z + y * z == 1 m.quadcon(2).Qrow = [1, 2]; m.quadcon(2).Qcol = [3, 3]; m.quadcon(2).Qval = [1.0, 1.0]; m.quadcon(2).q = sparse(3,1); m.quadcon(2).rhs = 1.0; m.quadcon(2).sense = '='; m.quadcon(2).name = 'bilinear1'; % Solve bilinear model, display solution. The problem is non-convex, % we need to set the parameter 'NonConvex' in order to solve it. params.NonConvex = 2; result = gurobi(m, params); disp(result.x); % Constrain 'x' to be integral and solve again m.vtype = 'ICC'; result = gurobi(m, params); disp(result.x); end