OATAO - Open Archive Toulouse Archive Ouverte Open Access Week

Worst-Case Complexity Bounds of Directional Direct-Search Methods for Multiobjective Optimization

Custódio, Ana Luísa and Diouane, Youssef and Garmanjani, Rohollah and Riccietti, Elisa Worst-Case Complexity Bounds of Directional Direct-Search Methods for Multiobjective Optimization. (2020) Journal of Optimization Theory and Applications. ISSN 0022-3239

[img] (Document in English)

PDF (Author's version) - Depositor and staff only until 23 May 2021 - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
489kB

Official URL: https://doi.org/10.1007/s10957-020-01781-z

Abstract

Direct Multisearch is a well-established class of algorithms, suited for multiobjective derivative-free optimization. In this work, we analyze the worst-case complexity of this class of methods in its most general formulation for unconstrained optimization. Considering nonconvex smooth functions, we show that to drive a given criticality measure below a specific positive threshold, Direct Multisearch takes at most a number of iterations proportional to the square of the inverse of the threshold, raised to the number of components of the objective function. This number is also proportional to the size of the set of linked sequences between the first unsuccessful iteration and the iteration immediately before the one where the criticality condition is satisfied. We then focus on a particular instance of Direct Multisearch, which considers a more strict criterion for accepting new nondominated points. In this case, we can establish a better worst-case complexity bound, simply proportional to the square of the inverse of the threshold, for driving the same criticality measure below the considered threshold.

Item Type:Article
HAL Id:hal-03040932
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Universidade Nova de Lisboa - UNL (PORTUGAL)
Laboratory name:
Statistics:download
Deposited On:04 Dec 2020 14:03

Repository Staff Only: item control page