I’m trying to find the saddle point of a function. I’ve programmed a function saddle below (but if you know of a library to find saddle points, please let me know). The idea is that the input function should be specified in a way such that the first argument is a vector for which the function is min…

Most constrained optimisation algorithms will give you the multipliers as well as the optimum

[image] cortner: There is even an old package that @pkofod and I played around with somewhere. I doubt it’s super robust, but could be fun to run some simple benchmarks on problems with known solution. If only we had all the time in the world :slight_smile:

What’s the package? I can try it.

[image] GitHub - cortner/ConstrainedOptim.jl Contribute to cortner/ConstrainedOptim.jl development by creating an account on GitHub. But it’s been abandoned for a long time.

Unless you are interested in algorithm development you should use a mainstream code- there are plenty of them.

I’m the other contributor, and I approve of this message :wink:

Hmmm… I’m having an exact the same problem as OP: a transition state on a 2D surface. I played around with Optim, but it failed to give a correct result, unless my initial guess is super good. At the end, I wrote a simple piece of code implementing Newton’s method. The initial guess was from a li…

If you have a small number of variables then you can try IntervalRootFinding.jl . Do you have a MWE?

[image] dpsanders: MWE Thanks for sugeeting IntervalRootFinding. It should be able to solve my ccurent problem, but in the future each dimension might be extend to N dimension (2 N-D arrays), so I guess it won’t work any more. What is MWE?

I meant a minimal example of a problem where you want to find a saddle point. What do you mean by 2 N-D arrays? If the problem has too many dimensions then indeed IntervalRootFinding.jl will not be able to solve it.

Finding saddle point

General Usage

stevengj May 27, 2020, 4:13pm 28

As I noted in another thread, given a local optimum computed by any method you can always find the Lagrange multipliers afterwards just by solving a small linear system.

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Finding saddle point

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