GCPWL.java
/* Copyright 2021, Gurobi Optimization, LLC This example formulates and solves the following simple model with PWL constraints: maximize sum c[j] * x[j] subject to sum A[i,j] * x[j] <= 0, for i = 0, ..., m-1 sum y[j] <= 3 y[j] = pwl(x[j]), for j = 0, ..., n-1 x[j] free, y[j] >= 0, for j = 0, ..., n-1 where pwl(x) = 0, if x = 0 = 1+|x|, if x != 0 Note 1. sum pwl(x[j]) <= b is to bound x vector and also to favor sparse x vector. Here b = 3 means that at most two x[j] can be nonzero and if two, then sum x[j] <= 1 2. pwl(x) jumps from 1 to 0 and from 0 to 1, if x moves from negative 0 to 0, then to positive 0, so we need three points at x = 0. x has infinite bounds on both sides, the piece defined with two points (-1, 2) and (0, 1) can extend x to -infinite. Overall we can use five points (-1, 2), (0, 1), (0, 0), (0, 1) and (1, 2) to define y = pwl(x) */ import gurobi.*; import java.util.*; public class GCPWL { public static void main(String[] args) { try { int n = 5; int m = 5; double c[] = { 0.5, 0.8, 0.5, 0.1, -1 }; double A[][] = { {0, 0, 0, 1, -1}, {0, 0, 1, 1, -1}, {1, 1, 0, 0, -1}, {1, 0, 1, 0, -1}, {1, 0, 0, 1, -1} }; double xpts[] = {-1, 0, 0, 0, 1}; double ypts[] = {2, 1, 0, 1, 2}; // Env and model GRBEnv env = new GRBEnv(); GRBModel model = new GRBModel(env); model.set(GRB.StringAttr.ModelName, "GCPWL"); // Add variables, set bounds and obj coefficients GRBVar[] x = model.addVars(n, GRB.CONTINUOUS); for (int i = 0; i < n; i++) { x[i].set(GRB.DoubleAttr.LB, -GRB.INFINITY); x[i].set(GRB.DoubleAttr.Obj, c[i]); } GRBVar[] y = model.addVars(n, GRB.CONTINUOUS); // Set objective to maximize model.set(GRB.IntAttr.ModelSense, GRB.MAXIMIZE); // Add linear constraints for (int i = 0; i < m; i++) { GRBLinExpr le = new GRBLinExpr(); for (int j = 0; j < n; j++) { le.addTerm(A[i][j], x[j]); } model.addConstr(le, GRB.LESS_EQUAL, 0, "cx" + i); } GRBLinExpr le1 = new GRBLinExpr(); for (int j = 0; j < n; j++) { le1.addTerm(1.0, y[j]); } model.addConstr(le1, GRB.LESS_EQUAL, 3, "cy"); // Add piecewise constraints for (int j = 0; j < n; j++) { model.addGenConstrPWL(x[j], y[j], xpts, ypts, "pwl" + j); } // Optimize model model.optimize(); for (int j = 0; j < n; j++) { System.out.println("x[" + j + "] = " + x[j].get(GRB.DoubleAttr.X)); } System.out.println("Obj: " + model.get(GRB.DoubleAttr.ObjVal)); // Dispose of model and environment model.dispose(); env.dispose(); } catch (GRBException e) { System.out.println("Error code: " + e.getErrorCode() + ". " + e.getMessage()); } } }
