The proximal point method with a vectorial Bregman regularization in multiobjective DC programming. (2nd January 2022)

• Record Type: Journal Article
• Authors: Souza, João Carlos de O.; Cruz Neto, João Xavier da; Lopes, Jurandir de Oliveira; Silva, Roberto Cristóvão Mesquita; Bitar, Sandro Dimy Barbosa
• Is Part Of: Optimization. Volume 71:Number 1(2022)
• Page Start: 263
• Page End: 284
• Publication Date: 2022-01-02
• Subjects: Proximal point method -- multiobjective optimization -- Bregman distance -- DC function; 49M37 -- 65K05 -- 90C26 -- 90C29; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1755862
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : For solving constrained multiobjective problems with a vector-valued DC (difference of convex) objective function, we consider a vectorial Bregman regularized proximal point method which extends both the scalar proximal point method for DC functions and the vectorial proximal point method for vector-valued convex functions. By using a vectorial regularization function, our method does not use auxiliary vectorial sequences to make the method a vectorial one but providing an extra flexibility to the method. Some encouraging numerical experiments are presented.