A comparison of methods for traversing regions of non-convexity in optimization problems

Michael Bartholomew-Biggs, Salah Beddiaf, Bruce Christianson

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Abstract

This paper considers the well-known problem of dealing with non-convexity during the minimization of a non-linear function f(x) by Newton-like methods. The proposal made here involves a curvilinear search along an approximation to the continuous steepest descent path defined by the solution of the differential equation The algorithm we develop and describe has some features in common with trust-region methods and we present some numerical experiments in which its performance is compared with other ODE-based and trust-region methods.

Original languageEnglish
Pages (from-to)1-23
Number of pages23
JournalNumerical Algorithms
Early online date13 Nov 2019
DOIs
Publication statusE-pub ahead of print - 13 Nov 2019

Keywords

  • Non-convex optimization, ODE-methods, Continuous steepest-descent path (CSDP), trust-region, Newton-like methods, curvilinear search.
  • Trust-region
  • Non-convex optimization
  • ODE-methods
  • Curvilinear search
  • Newton-like methods
  • Continuous steepest-descent path (CSDP)

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