I am really puzzled and also frustrated that no matter how simple the problem was, like one below, Ipopt returns
EXIT: Restoration Failed!
using JuMP
using Ipopt
model = Model(Ipopt.Optimizer)
@variable(model, x, start = 0.0)
@variable(model, y, start = 0.0)
@NLobjective(model, Min, (1 - x)^2 + 100 * (y - x^2)^2)
optimize!(model)
what did I do wrong? please help!
Your code works fine with JuMP (0.21.5) and Ipopt(0.6.5). Maybe you can update JuMP to version 0.21.5.
Yes, there was an issue with mumps. Please update
Thanks!
just want to report back that the issue got resolved. But I am not sure how I did it.
Basically first I updated to JuMP(0.21.5) as advised but still had the same issue.
then, I tried to update all packages and build all package again, but got errors associated with CUDA* about missing library.
so I removed all CUDA* related stuff and install latest NVidia CUDA library. Then I reinstalled CUDA*
and rebuild all packages.
after that, Ipopt issue seems went away.
Hi, now the EXIT: Restoration Failed issue was gone, but I am having strange optimal solution with the following example
using JuMP
using Ipopt
model = Model(Ipopt.Optimizer)
@variable(model, α, start=1.0 )
@variable(model, β, start=1.0 )
x = [1. 2.; 3. -1; 5.0 3.;6. 7.]
f(α, β) = maximum(sum([α β] .* x, dims=2))
g(α, β) = minimum(sum([α β] .* x, dims=2))
JuMP.register(model, :f, 2, f, autodiff=true)
JuMP.register(model, :g, 2, g, autodiff=true)
@NLobjective(model, Max, f(α, β) / g(α, β) )
optimize!(model)
output
Number of objective function evaluations = 368
Number of objective gradient evaluations = 12
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 = 0
Total CPU secs in IPOPT (w/o function evaluations) = 0.171
Total CPU secs in NLP function evaluations = 0.004
EXIT: Optimal Solution Found.
result:
julia> value(α)
-6.616112462703816e14
julia> value(β)
2.2053711899565838e14
julia> objective_value(model)
0.08333330892901637
however, this is definitely not good solution as even with start number 1, the objective could be 6.5. what is wrong with my formulation?
Ipopt is a solver for convex problems that are twice differentiable. Your problem doesn’t meet these requirements, and it has a divide-by-zero issue when g(a,b) = 0.
You should consider other ways of formulating this problem (e.g., as a MIP maximizing f(a,b) - g(a,b) where g(a, b) >= 0.000001 using this reformulation of max: 9 Mixed integer optimization — MOSEK Modeling Cookbook 3.3.0).
very nice! really appreciated! Exactly what I have been looking for! 