Inertial forward–backward methods for solving vector optimization problems. (3rd July 2018)

• Record Type: Journal Article
• Authors: Boţ, Radu Ioan; Grad, Sorin-Mihai
• Is Part Of: Optimization. Volume 67:Number 7(2018)
• Page Start: 959
• Page End: 974
• Publication Date: 2018-07-03
• Subjects: Vector optimization problems -- inertial proximal algorithms -- forward–backward algorithms -- weakly efficient solutions; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1440553
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: We propose two forward–backward proximal point type algorithms with inertial/memory effects for determining weakly efficient solutions to a vector optimization problem consisting in vector-minimizing with respect to a given closed convex pointed cone the sum of a proper cone-convex vector function with a cone-convex differentiable one, both mapping from a Hilbert space to a Banach one. Inexact versions of the algorithms, more suitable for implementation, are provided as well, while as a byproduct one can also derive a forward–backward method for solving the mentioned problem. Numerical experiments with the proposed methods are carried out in the context of solving a portfolio optimization problem.