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Complexity of gradient descent for multiobjective optimization

J. Fliege(J.Fliege***at***soton.ac.uk)
A. I. F. Vaz(aivaz***at***dps.uminho.pt)
L. N. Vicente(lnv***at***mat.uc.pt)

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 analyze 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.

Keywords: Multiobjective optimization, gradient descent, steepest descent, global rates, worst-case complexity

Category 1: Convex and Nonsmooth Optimization

Category 2: Nonlinear Optimization

Citation: J. Fliege, A. I. F. Vaz, and L. N. Vicente, Complexity of gradient descent for multiobjective optimization, preprint 18-12, Dept. Mathematics, Univ. Coimbra

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Entry Submitted: 04/17/2018
Entry Accepted: 04/17/2018
Entry Last Modified: 04/17/2018

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