forum.alglib.nethttp://forum.alglib.net/ Non-linear optimization problem near a local optimumhttp://forum.alglib.net/viewtopic.php?f=2&t=2509 Page 1 of 1

 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.Questions: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 knownuse minlmsetstpmax(minlmstate state, double stpmax); to reduce the step size, possibly at the cost of performanceinstead 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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