#!/usr/bin/env python3# Copyright 2025, 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)#importgurobipyasgpfromgurobipyimportGRBtry:n=5m=5c=[0.5,0.8,0.5,0.1,-1]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],]# Create a new modelmodel=gp.Model("gc_pwl")# Create variablesx=model.addVars(n,lb=-GRB.INFINITY,name="x")y=model.addVars(n,name="y")# Set objectivemodel.setObjective(gp.quicksum(c[j]*x[j]forjinrange(n)),GRB.MAXIMIZE)# Add Constraintsforiinrange(m):model.addConstr(gp.quicksum(A[i][j]*x[j]forjinrange(n))<=0)model.addConstr(y.sum()<=3)forjinrange(n):model.addGenConstrPWL(x[j],y[j],[-1,0,0,0,1],[2,1,0,1,2])# Optimize modelmodel.optimize()forjinrange(n):print(f"{x[j].VarName} ={x[j].X:g}")print(f"Obj:{model.ObjVal:g}")exceptgp.GurobiErrorase:print(f"Error code{e.errno}:{e}")exceptAttributeError:print("Encountered an attribute error")