piecewise.m
% Copyright 2016, Gurobi Optimization, Inc.
% This example considers the following separable, convex problem:
%
% minimize f(x) - y + g(z)
% subject to x + 2 y + 3 z <= 4
% x + y >= 1
% x, y, z <= 1
%
% where f(u) = exp(-u) and g(u) = 2 u^2 - 4 u, for all real u. It
% formulates and solves a simpler LP model by approximating f and
% g with piecewise-linear functions. Then it transforms the model
% into a MIP by negating the approximation for f, which corresponds
% to a non-convex piecewise-linear function, and solves it again.
names = {'x'; 'y'; 'z'};
try
clear model;
model.A = sparse([1 2 3; 1 1 0]);
model.obj = [0; -1; 0];
model.rhs = [4; 1];
model.sense = '<>';
model.vtype = 'C';
model.lb = [0; 0; 0];
model.ub = [1; 1; 1];
model.varnames = names;
% Compute f and g on 101 points in [0,1]
u = linspace(0.0, 1.0, 101);
f = exp(-u);
g = 2*u.^2 - 4*u;
% Set piecewise linear objective f(x)
model.pwlobj(1).var = 1;
model.pwlobj(1).x = u;
model.pwlobj(1).y = f;
% Set piecewise linear objective g(z)
model.pwlobj(2).var = 3;
model.pwlobj(2).x = u;
model.pwlobj(2).y = g;
% Optimize model as LP
result = gurobi(model);
disp(result);
for v=1:length(names)
fprintf('%s %d\n', names{v}, result.x(v));
end
fprintf('Obj: %e\n', result.objval);
% Negate piecewise-linear objective function for x
f = -f;
model.pwlobj(1).y = f;
gurobi_write(model, 'pwl.lp')
% Optimize model as a MIP
result = gurobi(model);
disp(result);
for v=1:length(names)
fprintf('%s %d\n', names{v}, result.x(v));
end
fprintf('Obj: %e\n', result.objval);
catch gurobiError
fprintf('Error reported\n');
end
