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I'm finding the literature on interior point methods somewhat inaccessible but I've found papers benchmarking different interior point methods for unconstrained nonlinear Nonconvex optimization. I can't find a comparison between interior point methods and a standard LBFGS. Since it looks like the interior point method packages use LBFGS, my guess is that this is not a proper comparison.

Are LBFGS and interior methods competing alternatives for unconstrained nonlinear nonconvex optimization? If not, what are the different nonlinear optimization problems they these methods address? When would one use a standard LBFGS vs interior point method for this problem? Is this too bleeding edge for a user of these packages to be looking into?

I'm intending to use this for problems with 100s-1000s of variables but I'm interested in a more general answer too.

Praxeolitic
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  • I'm not sure I follow. You have an unconstrained problem with $\approx 1000$ variables. What kind of IP were you looking at? IPs only make sense for constrained problems. Also, what is your goal? Local minima, global minima? – Nitish Mar 28 '14 at 21:14
  • Most of what I've seen for IP is constrained but there's a paper by Nocedal that benchmarks interior point packages for unconstrained as well as constrained nonlinear optimization. He comments that interior point methods become various Newton methods for unconstrained but then he does the benchmark anyway. I wasn't sure how to interpret that. I don't know enough about IP to have a specific kind that I want. I'm looking for local minima but if the optimizer has slack that lets it jump to lower minima that aren't strictly local that'd be even better. – Praxeolitic Mar 28 '14 at 21:28
  • @Praxeolitic do you remember the paper? – John Madden Jan 15 '23 at 03:27

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