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Nonlinearsolve.jl: Fast and Robust Solvers for Nonlinear Equations in Julia

arxiv.org

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Re: Nonlinearsolve.jl: Fast and Robust Solvers for Nonlinear Equations in Julia

#3

Post by adgjlsfhk1 »

wenc wrote: post #2

Would be interested to see this compared to IPOPT. https://coin-or.github.io/Ipopt/ IPOPT isn't tailored to NLEs specifically, but it does solve NLPs well. It also uses some amazing Fortran linear algebra routines from Harwell (MA57).

it should be pretty easy to add to the benchmarks. From a first glance, it looks like they have a lot of the necessary machinery to do well.

Re: Nonlinearsolve.jl: Fast and Robust Solvers for Nonlinear Equations in Julia

#4

Post by jpfr »

wenc wrote: post #2

Would be interested to see this compared to IPOPT. https://coin-or.github.io/Ipopt/ IPOPT isn't tailored to NLEs specifically, but it does solve NLPs well. It also uses some amazing Fortran linear algebra routines from Harwell (MA57).

This article is about “solving” differential equations and not convex optimization.

Re: Nonlinearsolve.jl: Fast and Robust Solvers for Nonlinear Equations in Julia

#5

Post by wenc »

jpfr wrote: post #4
wenc wrote: post #2

Would be interested to see this compared to IPOPT. https://coin-or.github.io/Ipopt/ IPOPT isn't tailored to NLEs specifically, but it does solve NLPs well. It also uses some amazing Fortran linear algebra routines from Harwell (MA57).

This article is about “solving” differential equations and not convex optimization.

> This article is about “solving” differential equations and not convex optimization.

This article is about solving nonlinear equations (not differential equations, not sure where you got that from). All NLP optimizers can solve nonlinear equations — it’s a special case where the objective is constant.

Ipopt is not a convex solver so am not sure what convex optimization you are referring to. It is a general nonlinear solver, which covers nonconvex problems as well (I worked on nonconvex nonlinear programs for a decade and it was my primary solver)

Also all nonlinear equation systems are nonconvex. (A convex program requires equality constraints to be linear)

Re: Nonlinearsolve.jl: Fast and Robust Solvers for Nonlinear Equations in Julia

#6

Post by FreakLegion »

wenc wrote: post #5
jpfr wrote: post #4

Earlier quoted context omitted.

This article is about “solving” differential equations and not convex optimization.

> This article is about “solving” differential equations and not convex optimization. This article is about solving nonlinear equations (not differential equations, not sure where you got that from). All NLP optimizers can solve nonlinear equations — it’s a special case where the objective is constant. Ipopt is not a convex solver so am not sure what convex optimization you are referring to. It is a general nonlinear…

> all nonlinear equation systems are nonconvex

Maybe you have something more particular in mind when you say "systems", but not all nonlinear functions are non-convex. Least squares, for example, is nonlinear and convex.

Also note that IPOPT, while wonderful, is a local solver. It may not be limited to convex problems, but those are the only ones it's guaranteed to solve to optimality.

Re: Nonlinearsolve.jl: Fast and Robust Solvers for Nonlinear Equations in Julia

#7

Post by Bimos »

FreakLegion wrote: post #6
wenc wrote: post #5

Earlier quoted context omitted.

> This article is about “solving” differential equations and not convex optimization. This article is about solving nonlinear equations (not differential equations, not sure where you got that from). All NLP optimizers can solve nonlinear equations — it’s a special case where the objective is constant. Ipopt is not a convex solver so am not sure what convex optimization you are referring to. It is a general nonlinear…

> all nonlinear equation systems are nonconvex Maybe you have something more particular in mind when you say "systems", but not all nonlinear functions are non-convex. Least squares, for example, is nonlinear and convex. Also note that IPOPT, while wonderful, is a local solver. It may not be limited to convex problems, but those are the only ones it's guaranteed to solve to optimality.

The feasible region {x | f(x) = 0} is nonconvex no matter whether f is convex.

Re: Nonlinearsolve.jl: Fast and Robust Solvers for Nonlinear Equations in Julia

#10

Post by eigenspace »

Bimos wrote: post #8

On GPU, it can only solve small instances which one single GPU thread can handle, and can only benefit from GPU by solving multiple instances, right?

That's the GPU parallelization they offer, but if you had a problem where say the objective function itself was really big and cumbersome and benefited from GPU parallelization, then you could put that objective function on the GPU just fine.

I think this use case isn't really discussed in the paper because the solver doesn't need to specialize on that case, it should 'just work' without any intervention needed.

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