A superlinearly convergent nonmonotone quasi-Newton method for unconstrained multiobjective optimization. (1st November 2020)

• Record Type: Journal Article
• Authors: Mahdavi-Amiri, N.; Salehi Sadaghiani, F.
• Is Part Of: Optimization methods and software. Volume 35:Number 6(2020)
• Page Start: 1223
• Page End: 1247
• Publication Date: 2020-11-01
• Subjects: Multiobjective programming -- nonmonotone line search algorithm -- nonmonotone quasi-Newton method -- efficiency; 90C29 -- 90C30 -- 90C53; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2020.1737691
• Languages: English
• ISSNs: 1055-6788

Abstract

ABSTRACT: We propose and analyse a nonmonotone quasi-Newton algorithm for unconstrained strongly convex multiobjective optimization. In our method, we allow for the decrease of a convex combination of recent function values. We establish the global convergence and local superlinear rate of convergence under reasonable assumptions. We implement our scheme in the context of BFGS quasi-Newton method for solving unconstrained multiobjective optimization problems. Our numerical results show that the nonmonotone quasi-Newton algorithm uses fewer function evaluations than the monotone quasi-Newton algorithm.