piecewise_cs.cs
/* Copyright 2021, Gurobi Optimization, LLC */ /* 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. */ using System; using Gurobi; class piecewise_cs { private static double f(double u) { return Math.Exp(-u); } private static double g(double u) { return 2 * u * u - 4 * u; } static void Main() { try { // Create environment GRBEnv env = new GRBEnv(); // Create a new model GRBModel model = new GRBModel(env); // Create variables double lb = 0.0, ub = 1.0; GRBVar x = model.AddVar(lb, ub, 0.0, GRB.CONTINUOUS, "x"); GRBVar y = model.AddVar(lb, ub, 0.0, GRB.CONTINUOUS, "y"); GRBVar z = model.AddVar(lb, ub, 0.0, GRB.CONTINUOUS, "z"); // Set objective for y model.SetObjective(-y); // Add piecewise-linear objective functions for x and z int npts = 101; double[] ptu = new double[npts]; double[] ptf = new double[npts]; double[] ptg = new double[npts]; for (int i = 0; i < npts; i++) { ptu[i] = lb + (ub - lb) * i / (npts - 1); ptf[i] = f(ptu[i]); ptg[i] = g(ptu[i]); } model.SetPWLObj(x, ptu, ptf); model.SetPWLObj(z, ptu, ptg); // Add constraint: x + 2 y + 3 z <= 4 model.AddConstr(x + 2 * y + 3 * z <= 4.0, "c0"); // Add constraint: x + y >= 1 model.AddConstr(x + y >= 1.0, "c1"); // Optimize model as an LP model.Optimize(); Console.WriteLine("IsMIP: " + model.IsMIP); Console.WriteLine(x.VarName + " " + x.X); Console.WriteLine(y.VarName + " " + y.X); Console.WriteLine(z.VarName + " " + z.X); Console.WriteLine("Obj: " + model.ObjVal); Console.WriteLine(); // Negate piecewise-linear objective function for x for (int i = 0; i < npts; i++) { ptf[i] = -ptf[i]; } model.SetPWLObj(x, ptu, ptf); // Optimize model as a MIP model.Optimize(); Console.WriteLine("IsMIP: " + model.IsMIP); Console.WriteLine(x.VarName + " " + x.X); Console.WriteLine(y.VarName + " " + y.X); Console.WriteLine(z.VarName + " " + z.X); Console.WriteLine("Obj: " + model.ObjVal); // Dispose of model and environment model.Dispose(); env.Dispose(); } catch (GRBException e) { Console.WriteLine("Error code: " + e.ErrorCode + ". " + e.Message); } } }
