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

Michael Bartholomew-Biggs; Salah Beddiaf; Bruce Christianson

doi:10.1007/s11075-019-00811-w

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 language	English
Pages (from-to)	1-23
Number of pages	23
Journal	Numerical Algorithms
Early online date	13 Nov 2019
DOIs	https://doi.org/10.1007/s11075-019-00811-w
Publication status	E-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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10.1007/s11075-019-00811-wLicence: Other

Paper_Septemebr_9
© Springer Science+Business Media, LLC, part of Springer Nature 2019. This is a post-peer-review, pre-copyedit version of an article published in Numerical Algorithms. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11075-019-00811-w.
Accepted author manuscript, 875 KBLicence: Other

Cite this

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

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Keywords

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