JuMP & Ipopt: failed to converge solution for standard Rosenbrock

Specific Domains Optimization (Mathematical)
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1

Hi everyone, I am new to Julia (and programming in general). I encountered an error while using JuMP and Ipopt to solve unconstrained maximization for a standard Rosenbrock function. It reports that “EXIT: Optimal Solution Found” but “Optimization failed or stopped early: LOCALLY_SOLVED”. (or if directly using value(x) after optimization, then reported objects of type FLOT64 are not callable

I literally copied the codes, so I am really curious about what else can go wrong.

Any help is much appreciated!

using JuMP
using Ipopt

model = Model(Ipopt.Optimizer)

@variable(model, x, start = 0.0)
@variable(model, y, start = 0.0)

# Define the objective function
@objective(model, Min, (1 - x)^2 + 100 * (y - x^2)^2)

JuMP.optimize!(model)

if termination_status(model) == MOI.OPTIMAL
    println("Optimal value of x: ", value(x))
    println("Optimal value of y: ", value(y))
else
    println("Optimization failed or stopped early: ", termination_status(model))
end
2

Hi @GY3090, welcome to the forum :smile:

I literally copied the codes, so I am really curious about what else can go wrong.

Ooo! Copied from where? We should fix the documentation.

Here’s the link to the official JuMP documentation: Simple examples · JuMP

There are a few things to fix with your code:

Ipopt is a local solver, so it cannot prove the solution is OPTIMAL. Do instead

if termination_status(model) == LOCALLY_SOLVED
    println("Optimal value of x: ", value(x))
    println("Optimal value of y: ", value(y))
else
    println("Optimization failed or stopped early: ", termination_status(model))
end

There are quite a few complexities with the various statuses, so if you are new to Julia and programming, just use:

if is_solved_and_feasible(model)
    println("Optimal value of x: ", value(x))
    println("Optimal value of y: ", value(y))
else
    println("Optimization failed or stopped early: ", termination_status(model))
end

Here’s what I get when I run that code:

julia> using JuMP

julia> using Ipopt

julia> begin
           model = Model(Ipopt.Optimizer)
           @variable(model, x, start = 0.0)
           @variable(model, y, start = 0.0)
           @objective(model, Min, (1 - x)^2 + 100 * (y - x^2)^2)
           optimize!(model)
           if is_solved_and_feasible(model)
               println("Optimal value of x: ", value(x))
               println("Optimal value of y: ", value(y))
           else
               println("Optimization failed or stopped early: ", termination_status(model))
           end
       end
This is Ipopt version 3.14.17, running with linear solver MUMPS 5.7.3.

Number of nonzeros in equality constraint Jacobian...:        0
Number of nonzeros in inequality constraint Jacobian.:        0
Number of nonzeros in Lagrangian Hessian.............:        3

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  1.0000000e+00 0.00e+00 2.00e+00  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0
   1  9.5312500e-01 0.00e+00 1.25e+01  -1.0 1.00e+00    -  1.00e+00 2.50e-01f  3
   2  4.8320569e-01 0.00e+00 1.01e+00  -1.0 9.03e-02    -  1.00e+00 1.00e+00f  1
   3  4.5708829e-01 0.00e+00 9.53e+00  -1.0 4.29e-01    -  1.00e+00 5.00e-01f  2
   4  1.8894205e-01 0.00e+00 4.15e-01  -1.0 9.51e-02    -  1.00e+00 1.00e+00f  1
   5  1.3918726e-01 0.00e+00 6.51e+00  -1.7 3.49e-01    -  1.00e+00 5.00e-01f  2
   6  5.4940990e-02 0.00e+00 4.51e-01  -1.7 9.29e-02    -  1.00e+00 1.00e+00f  1
   7  2.9144630e-02 0.00e+00 2.27e+00  -1.7 2.49e-01    -  1.00e+00 5.00e-01f  2
   8  9.8586451e-03 0.00e+00 1.15e+00  -1.7 1.10e-01    -  1.00e+00 1.00e+00f  1
   9  2.3237475e-03 0.00e+00 1.00e+00  -1.7 1.00e-01    -  1.00e+00 1.00e+00f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  10  2.3797236e-04 0.00e+00 2.19e-01  -1.7 5.09e-02    -  1.00e+00 1.00e+00f  1
  11  4.9267371e-06 0.00e+00 5.95e-02  -1.7 2.53e-02    -  1.00e+00 1.00e+00f  1
  12  2.8189506e-09 0.00e+00 8.31e-04  -2.5 3.20e-03    -  1.00e+00 1.00e+00f  1
  13  9.6379889e-16 0.00e+00 8.68e-07  -5.7 9.78e-05    -  1.00e+00 1.00e+00f  1
  14  3.0814879e-29 0.00e+00 2.02e-13  -8.6 4.65e-08    -  1.00e+00 1.00e+00f  1

Number of Iterations....: 14

                                   (scaled)                 (unscaled)
Objective...............:   3.0814879110195774e-29    3.0814879110195774e-29
Dual infeasibility......:   2.0183854587685121e-13    2.0183854587685121e-13
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.......:   2.0183854587685121e-13    2.0183854587685121e-13


Number of objective function evaluations             = 36
Number of objective gradient evaluations             = 15
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             = 14
Total seconds in IPOPT                               = 0.005

EXIT: Optimal Solution Found.
Optimal value of x: 0.9999999999999899
Optimal value of y: 0.9999999999999792

Your objects of type Float64 are not callable error is not related to the code you have posted. This happens if you have

julia> value = 1.0
1.0

julia> value(1)
ERROR: MethodError: objects of type Float64 are not callable
Maybe you forgot to use an operator such as *, ^, %, / etc. ?
Stacktrace:
[1] top-level scope
@ REPL[2]:1
3

I see the problem! Thank you, and it works :slight_smile: I copied the part from an unofficial source, so maybe there are some misunderstandings.

4

No problem. Let me know if you have any other questions.

If you’re new to Julia and programming, you may want to check out our “getting started” tutorials: Getting started with Julia · JuMP