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Complexity of gradient descent for multiobjective optimization

Complexity of gradient descent for multiobjective optimization
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 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.
1055-6788
Fliege, J.
54978787-a271-4f70-8494-3c701c893d98
Vaz, A.I.F.
d162bdcd-993d-4fe6-a63f-19cb574dcd51
Vicente, L.N.
84df3627-cdb1-483c-a593-4fad27142a19
Fliege, J.
54978787-a271-4f70-8494-3c701c893d98
Vaz, A.I.F.
d162bdcd-993d-4fe6-a63f-19cb574dcd51
Vicente, L.N.
84df3627-cdb1-483c-a593-4fad27142a19

Fliege, J., Vaz, A.I.F. and Vicente, L.N. (2018) Complexity of gradient descent for multiobjective optimization. Optimization Methods and Software. (doi:10.1080/10556788.2018.1510928).

Record type: Article

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.

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Accepted/In Press date: 2 August 2018
e-pub ahead of print date: 29 August 2018

Identifiers

Local EPrints ID: 423833
URI: http://eprints.soton.ac.uk/id/eprint/423833
ISSN: 1055-6788
PURE UUID: 0a553ac2-955a-4fe8-949a-fe391c0020ab
ORCID for J. Fliege: ORCID iD orcid.org/0000-0002-4459-5419

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Date deposited: 02 Oct 2018 16:30
Last modified: 18 Feb 2021 17:11

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