Non-linear optimization problem near a local optimum
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Author:  johan [ Tue Jul 07, 2015 6:03 pm ]
Post subject:  Non-linear optimization problem near a local optimum

Problem (this is not a "homework" problem but a "minimum working example" of the problem that I think I have. My problem can only be solved using least-square-ish approaches):

Using f(x) = sin(x), find the solution for f(x) = 0 using the Levenberg-Marquardt (LM) argorithm that is closest to x = 0.9 * (pi/2) as initial guess. Hence, a local optimum is searched for.

The expected solution is x = 0. However, the alglib implementation of LM yields -18.85, which numerically represents -6 * pi.

Further, assume that:
  • The initial guess cannot be improved, i.e. it cannot be brought closer to the expected solution.

  • In this problem related with the fact that f is locally concave around the initial guess?
  • What (alglib) (optimization) procedure is recommended to obtain the expected solution?


The following can help to obtain the correct solution:
  • use minlmsetbc(minlmstate state, double[] bndl, double[] bndu) if the bounds of x are known
  • use minlmsetstpmax(minlmstate state, double stpmax); to reduce the step size, possibly at the cost of performance
  • instead of LM, use a trust-region method (?)

But what if bounds and/or step size information is not available?


Many thanks in advance!

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