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gc_pwl.py
#!/usr/bin/env python3.7 # 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 gurobipy as gp from gurobipy import GRB try: n = 5 m = 5 c = [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 model model = gp.Model("gc_pwl") # Create variables x = model.addVars(n, lb=-GRB.INFINITY, name="x") y = model.addVars(n, name="y") # Set objective model.setObjective(gp.quicksum(c[j]*x[j] for j in range(n)), GRB.MAXIMIZE) # Add Constraints for i in range(m): model.addConstr(gp.quicksum(A[i][j]*x[j] for j in range(n)) <= 0) model.addConstr(y.sum() <= 3) for j in range(n): model.addGenConstrPWL(x[j], y[j], [-1, 0, 0, 0, 1], [2, 1, 0, 1, 2]) # Optimize model model.optimize() for j in range(n): print('%s = %g' % (x[j].varName, x[j].x)) print('Obj: %g' % model.objVal) except gp.GurobiError as e: print('Error code ' + str(e.errno) + ": " + str(e)) except AttributeError: print('Encountered an attribute error')