A proximal gradient splitting method for solving convex vector optimization problems. (2nd January 2022)

• Record Type: Journal Article
• Authors: Bello-Cruz, Yunier; Melo, Jefferson G.; Serra, Ray V.G.
• Is Part Of: Optimization. Volume 71:Number 1(2022)
• Page Start: 33
• Page End: 53
• Publication Date: 2022-01-02
• Subjects: Convex programming -- full convergence -- proximal gradient method -- Vector optimization; 49J52 -- 90C25 -- 90C52 -- 65K05; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1800699
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, a proximal gradient splitting method for solving nondifferentiable vector optimization problems is proposed. The convergence analysis is carried out when the objective function is the sum of two convex functions where one of them is assumed to be continuously differentiable. The proposed splitting method exhibits full convergence to a weakly efficient solution without assuming the Lipschitz continuity of the Jacobian of the differentiable component. To carry this analysis, the popular Beck–Teboulle's line-search procedure is extended to the vectorial setting under mild assumptions. It is also shown that the proposed scheme obtains an ϵ -approximate solution to the vector optimization problem in at most O ( 1 / ε ) iterations.