Complexity of gradient descent for multiobjective optimization. (3rd September 2019)

• Record Type: Journal Article
• Authors: Fliege, J.; Vaz, A. I. F.; Vicente, L. N.
• Is Part Of: Optimization methods and software. Volume 34:Number 5(2019)
• Page Start: 949
• Page End: 959
• Publication Date: 2019-09-03
• Subjects: Multiobjective optimization -- gradient descent -- steepest descent -- global rates -- worst-case complexity; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2018.1510928
• Languages: English
• ISSNs: 1055-6788

Abstract

ABSTRACT: A number of first-order methods have been proposed for smooth multiobjective optimization for which some form of convergence to first-order criticality has been proved. Such convergence is global in the sense of being independent of the starting point. In this paper, we analyse the rate of convergence of gradient descent for smooth unconstrained multiobjective optimization, and we do it for non-convex, convex, and strongly convex vector functions. These global rates are shown to be the same as for gradient descent in single-objective optimization and correspond to appropriate worst-case complexity bounds. In the convex cases, the rates are given for implicit scalarizations of the problem vector function.