GCMMA using NLopt

Specific Domains Optimization (Mathematical)
1

Hi All. I have a question can i use NLopt for GCMMA algorithm?
also one other question can zygote has errors in calculating gradients?
thank you

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Yes, the NLopt.LD_MMA algorithm in NLopt is the “globally convergent” variant of MMA by Svanberg (2002). (These days, I would tend to use the NLopt.LD_CCSAQ algorithm instead, which is another variant of the Svanberg algorithm.)

Nonconvex.jl also implements this method.

3

however, It is mentioned in NLopt documents that it is not using ptof. Svanberg algorithm. aslo as it is LD i though that it is local not global. right?

4

I don’t know what you are referring to. The NLopt manual specifically says it is using the Svanberg (2002) algorithm.

It is “LD” because the Svanberg algorithm is a local-optimization algorithm. I think you’re misunderstanding the meaning of the term “globally convergent”. “Globally convergent” does not mean that the algorithm necessarily converges to a global optimum. What it means is that the algorithm is guaranteed to converges to a local optimum from any feasible starting point (i.e. from any starting point satisfying the constraints).

(If you’re doing high-dimensional optimization of arbitrary non-convex functions, as is usually the case in PDE-constrained topology optimization, there is no practical optimization algorithm with any useful guarantees of attaining a global optimum. There are algorithms that converge to a global optimum eventually, of course — even random search does that — but they may take an arbitrarily long time and give no useful indication of when the global optimum is found.)

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5

ok thank you! i think i just get misunderstood from this sentence "The MMA implementation in NLopt, however, is completely independent of Svanberg’s, whose code we have not examined; any bugs are my own, of course.)"

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NLopt uses Svanberg’s published mathematical algorithm, it just doesn’t use his code (for copyright reasons).

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