Gurobi non-linear example

Gurobi supports a certain list of non-linear problems, e.g. sin, cos, min, max, power, exp, log

This is a sample script from Gurobi website

# This example considers the following nonconvex nonlinear problem

#

#  minimize   sin(x) + cos(2*x) + 1

#  subject to  0.25*exp(x) - x <= 0

#              -1 <= x <= 4

#

#  We show you two approaches to solve it as a nonlinear model:

#

#  1) Set the paramter FuncNonlinear = 1 to handle all general function

#     constraints as true nonlinear functions.

#

#  2) Set the attribute FuncNonlinear = 1 for each general function

#     constraint to handle these as true nonlinear functions.

#

import gurobipy as gp

from gurobipy import GRB

def printsol(m, x):

    print(f"x = {x.X}")

    print(f"Obj = {m.ObjVal}")

try:

    # Create a new model

    m = gp.Model()

    # Create variables

    x = m.addVar(lb=-1, ub=4, name="x")

    twox = m.addVar(lb=-2, ub=8, name="2x")

    sinx = m.addVar(lb=-1, ub=1, name="sinx")

    cos2x = m.addVar(lb=-1, ub=1, name="cos2x")

    expx = m.addVar(name="expx")

    # Set objective

    m.setObjective(sinx + cos2x + 1, GRB.MINIMIZE)

    # Add linear constraints

    lc1 = m.addConstr(0.25 * expx - x <= 0)

    lc2 = m.addConstr(2.0 * x - twox == 0)

    # Add general function constraints

    # sinx = sin(x)

    gc1 = m.addGenConstrSin(x, sinx, "gc1")

    # cos2x = cos(twox)

    gc2 = m.addGenConstrCos(twox, cos2x, "gc2")

    # expx = exp(x)

    gc3 = m.addGenConstrExp(x, expx, "gc3")

    # Approach (1) Set FuncNonlinear parameter

    m.params.FuncNonlinear = 1

    # Optimize the model

    m.optimize()

    printsol(m, x)

    # Restore unsolved state and set parameter FuncNonlinear to

    # its default value

    m.reset()

    m.resetParams()

    # Approach (2) Set FuncNonlinear attribute for every

    #             general function constraint

    gc1.FuncNonlinear = 1

    gc2.FuncNonlinear = 1

    gc3.FuncNonlinear = 1

    m.optimize()

    printsol(m, x)

except gp.GurobiError as e:

    print(f"Error code {e.errno}: {e}")

except AttributeError:

    print("Encountered an attribute error")