Try our new documentation site (beta).


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')

Try Gurobi for Free

Choose the evaluation license that fits you best, and start working with our Expert Team for technical guidance and support.

Evaluation License
Get a free, full-featured license of the Gurobi Optimizer to experience the performance, support, benchmarking and tuning services we provide as part of our product offering.
Academic License
Gurobi supports the teaching and use of optimization within academic institutions. We offer free, full-featured copies of Gurobi for use in class, and for research.
Cloud Trial

Request free trial hours, so you can see how quickly and easily a model can be solved on the cloud.

Search

Gurobi Optimization