piecewise.py
#!/usr/bin/env python3.7 # 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. import gurobipy as gp from math import exp def f(u): return exp(-u) def g(u): return 2 * u * u - 4 * u try: # Create a new model m = gp.Model() # Create variables lb = 0.0 ub = 1.0 x = m.addVar(lb, ub, name='x') y = m.addVar(lb, ub, name='y') z = m.addVar(lb, ub, name='z') # Set objective for y m.setObjective(-y) # Add piecewise-linear objective functions for x and z npts = 101 ptu = [] ptf = [] ptg = [] for i in range(npts): ptu.append(lb + (ub - lb) * i / (npts - 1)) ptf.append(f(ptu[i])) ptg.append(g(ptu[i])) m.setPWLObj(x, ptu, ptf) m.setPWLObj(z, ptu, ptg) # Add constraint: x + 2 y + 3 z <= 4 m.addConstr(x + 2 * y + 3 * z <= 4, 'c0') # Add constraint: x + y >= 1 m.addConstr(x + y >= 1, 'c1') # Optimize model as an LP m.optimize() print('IsMIP: %d' % m.IsMIP) for v in m.getVars(): print('%s %g' % (v.VarName, v.X)) print('Obj: %g' % m.ObjVal) print('') # Negate piecewise-linear objective function for x for i in range(npts): ptf[i] = -ptf[i] m.setPWLObj(x, ptu, ptf) # Optimize model as a MIP m.optimize() print('IsMIP: %d' % m.IsMIP) for v in m.getVars(): print('%s %g' % (v.VarName, v.X)) print('Obj: %g' % m.ObjVal) except gp.GurobiError as e: print('Error code ' + str(e.errno) + ": " + str(e)) except AttributeError: print('Encountered an attribute error')
