Complexity of gradient descent for multiobjective optimization

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 convergen...

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Bibliographic Details
Published inOptimization methods & software Vol. 34; no. 5; pp. 949 - 959
Main Authors Fliege, J., Vaz, A. I. F., Vicente, L. N.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 03.09.2019
Taylor and Francis
Taylor & Francis Ltd
Subjects
Complexity
Convergence
Global rates
Gradient descent
Mathematical programming
Multiobjective optimization
Multiple objective analysis
Optimization
Pareto optimum
Science & Technology
Steepest descent
worst-case complexity
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Summary: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.
ISSN:1055-6788
1029-4937
DOI:10.1080/10556788.2018.1510928