An incremental descent method for multi-objective optimization. (4th March 2023)

• Record Type: Journal Article
• Authors: Oliveira, Ivo F. D.; Takahashi, Ricardo H. C.
• Is Part Of: Optimization methods and software. Volume 38:Number 2(2023)
• Page Start: 312
• Page End: 331
• Publication Date: 2023-03-04
• Subjects: Gradient descent -- multi-objective optimization -- complexity reduction; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2022.2124989
• Languages: English
• ISSNs: 1055-6788

Abstract

ABSTRACT: Multi-objective steepest descent, under the assumption of lower-bounded objective functions with L -Lipschitz continuous gradients, requires O ( m / ϵ 2 ) gradient and function computations to produce a measure of proximity to critical conditions akin to | | ∇ f ( x ) | | ≤ ϵ in the single-objective setting, where m is the number of objectives considered. We reduce this to O ( 1 / ϵ 2 ) with a multi-objective incremental approach that has a computational cost that does not grow with the number of objective functions m .