This tutorial uses

  • python 3.11.4
  • casadi 3.6.3

Consider the unconstrained optimization problem whose objective us defined as,

$f(x)=(x-5^2)+(y-8)^2$

This is a convex problem with global solution $(x^{*},y^{*})=(5,8)$. The following code computes the solution to this problem numerically using IPOPT, an interior-point solver.

Its worth noting the following features of the Opti class.

  1. A modelling language for solving nonlinear optimization problem
  2. Interface to several solvers
  3. JIT evaluation
import casadi as cs
p=cs.Opti()
w=p.variables(1,2)
x=w[0]
y=w[1]
obj=(x-5)**2+(y-8)**2
p.minimize(obj)
p.solver('ipopt')
sol=p.solve()
print('x*: ',sol.value(x),'x*: ',sol.value(x))

******************************************************************************
This program contains Ipopt, a library for large-scale nonlinear optimization.
 Ipopt is released as open source code under the Eclipse Public License (EPL).
         For more information visit https://github.com/coin-or/Ipopt
******************************************************************************

This is Ipopt version 3.14.11, running with linear solver MUMPS 5.4.1.

Number of nonzeros in equality constraint Jacobian...:        0
Number of nonzeros in inequality constraint Jacobian.:        0
Number of nonzeros in Lagrangian Hessian.............:        2

Total number of variables............................:        2
                     variables with only lower bounds:        0
                variables with lower and upper bounds:        0
                     variables with only upper bounds:        0
Total number of equality constraints.................:        0
Total number of inequality constraints...............:        0
        inequality constraints with only lower bounds:        0
   inequality constraints with lower and upper bounds:        0
        inequality constraints with only upper bounds:        0

iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
   0  8.9000000e+01 0.00e+00 1.60e+01  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0
   1  0.0000000e+00 0.00e+00 0.00e+00  -1.0 8.00e+00    -  1.00e+00 1.00e+00f  1

Number of Iterations....: 1

                                   (scaled)                 (unscaled)
Objective...............:   0.0000000000000000e+00    0.0000000000000000e+00
Dual infeasibility......:   0.0000000000000000e+00    0.0000000000000000e+00
Constraint violation....:   0.0000000000000000e+00    0.0000000000000000e+00
Variable bound violation:   0.0000000000000000e+00    0.0000000000000000e+00
Complementarity.........:   0.0000000000000000e+00    0.0000000000000000e+00
Overall NLP error.......:   0.0000000000000000e+00    0.0000000000000000e+00


Number of objective function evaluations             = 2
Number of objective gradient evaluations             = 2
Number of equality constraint evaluations            = 0
Number of inequality constraint evaluations          = 0
Number of equality constraint Jacobian evaluations   = 0
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations             = 1
Total seconds in IPOPT                               = 0.023

EXIT: Optimal Solution Found.
      solver  :   t_proc      (avg)   t_wall      (avg)    n_eval
       nlp_f  |        0 (       0)  10.00us (  5.00us)         2
  nlp_grad_f  |        0 (       0) 290.00us ( 96.67us)         3
  nlp_hess_l  |        0 (       0)   6.00us (  6.00us)         1
       total  |  40.00ms ( 40.00ms)  31.65ms ( 31.65ms)         1
x*:  5.0 x*:  5.0