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On Necessary Optimality Conditions for Sets of Points in Multiobjective Optimization.

Authors :
Cristofari, Andrea
De Santis, Marianna
Lucidi, Stefano
Source :
Journal of Optimization Theory & Applications. Oct2024, Vol. 203 Issue 1, p126-145. 20p.
Publication Year :
2024

Abstract

Taking inspiration from what is commonly done in single-objective optimization, most local algorithms proposed for multiobjective optimization extend the classical iterative scalar methods and produce sequences of points able to converge to single efficient points. Recently, a growing number of local algorithms that build sequences of sets has been devised, following the real nature of multiobjective optimization, where the aim is that of approximating the efficient set. This calls for a new analysis of the necessary optimality conditions for multiobjective optimization. We explore conditions for sets of points that share the same features of the necessary optimality conditions for single-objective optimization. On the one hand, from a theoretical point of view, these conditions define properties that are necessarily satisfied by the (weakly) efficient set. On the other hand, from an algorithmic point of view, any set that does not satisfy the proposed conditions can be easily improved by using first-order information on some objective functions. We analyse both the unconstrained and the constrained case, giving some examples. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00223239
Volume :
203
Issue :
1
Database :
Academic Search Index
Journal :
Journal of Optimization Theory & Applications
Publication Type :
Academic Journal
Accession number :
180628862
Full Text :
https://doi.org/10.1007/s10957-024-02478-3