Exploting problem structure in Derivative-Free Optimization

Margherita Porcelli, Philippe Toint

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Abstract

A structured version of derivative-free random pattern search optimization algorithms is introduced which is able to exploit coordinate partially
separable structure (typically associated with sparsity) often present in
unconstrained and bound-constrained optimization problems. This technique
improves performance by orders of magnitude and makes it possible to solve
large problems that otherwise are totally intractable by other derivative-free
methods. A library of interpolation-based modelling tools is also described,
which can be associated to the structured or unstructured versions of the
initial BFO pattern search algorithm. The use of the library further enhances
performance, especially when associated with structure. The significant gains
in performance associated with these two techniques are illustrated using a
new freely-available release of BFO which incorporates them. A interesting
conclusion of the results presented is that providing global structural
information on a problem can result in significantly less evaluations of the
objective function than attempting to building local Taylor-like models.
Original languageEnglish
Article number6
Number of pages25
JournalACM Transactions on Mathematical Software
Volume48
Issue number1
Publication statusPublished - 26 Feb 2022

Keywords

  • derivative-free optimization
  • direct-search methods
  • structured problems
  • interpolation models

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