Invalid number in NLP function or derivative detected. about ipopt.jl HOT 8 CLOSED

It means that Ipopt tried to evaluate the objective at a point in the domain where the function or its derivative was undefined.

This is known and expected behavior and is not a bug. Ipopt assumes the function is defined and twice differentiable at all points in the variable domain, in Float64 precision.

Note that even if you have other constraints (like your quadratic) that should prevent this, Ipopt may evaluate infeasible points during the iteration process.

There are two likely cases:

• Very large value of x causing exp(Ax) to be Inf
• Very small value of sum(...), causing the derivative of log() to be very large (probably Inf).

To fix, try adding variable bounds to x to keep it in a reasonable domain.

BARON does't encounter this issue because it uses a different algorithm.

Instead of using Ipopt, you could also try formulating this as a conic program. It looks like you might have tried this since you mentioned MOSEK, but if you have trouble, please post on https://discourse.julialang.org/c/domain/opt/13.

The tricks you'll need are

• https://jump.dev/JuMP.jl/dev/tutorials/conic/tips_and_tricks/#Log-sum-exp
• https://jump.dev/JuMP.jl/dev/tutorials/conic/tips_and_tricks/#Second-Order-Cone

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Thank you for your reply! This makes great sense to me. MOSEK wouldn't work in this specific example as I am maximizing the convex logsumexp function, but I indeed apply the exp-cone reformulation trick for its minimization. Moreover, BARON typically suffers from exploding exp terms. So, I think this probably is due to small values of sum(...). I will confirm this, but I am closing the issue.

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Ah. I missed reading the Max. I just assumed you meant Min.

Ipopt also assumes that the problem is convex, so if you pass it a non-convex problem, anything can happen.

Does it make sense to maximize log-sum-exp? Ipopt will also have trouble with large exp.

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Thank you for your reply! From Ipopt my only hope is a decent solution, not global. In my research, I am showing some cases where maximizing logsumexp (or convex functions, in general) is useful in ML.

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From Ipopt my only hope is a decent solution, not global

Yeah so then I'd suggest: tight bounds, and a few different starting points.

In my research, I am showing some cases where maximizing logsumexp (or convex functions, in general) is useful in ML.

Interesting 🤔

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Yeah so then I'd suggest: tight bounds, and a few different starting points.

Exactly! Many random starting points and prayers :)

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You can check if Ipopt found a solution by looking at termination_status(model). I think it returns NUMERICAL_ERROR if it encountered a problem like that. (But you should double check.)

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Great to know, thank you very much for your support!

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