Convergence Rate of Gradient Descent Method for Multi-Objective Optimization

Convergence Rate of Gradient Descent Method for Multi-Objective Optimization

Year:    2019

Author:    Liaoyuan Zeng, Yuhong Dai, Yakui Huang

Journal of Computational Mathematics, Vol. 37 (2019), Iss. 5 : pp. 689–703

Abstract

The convergence rate of the gradient descent method is considered for unconstrained multi-objective optimization problems (MOP). Under standard assumptions, we prove that the gradient descent method with constant step sizes converges sublinearly when the objective functions are convex and the convergence rate can be strengthened to be linear if the objective functions are strongly convex. The results are also extended to the gradient descent method with the Armijo line search. Hence, we see that the gradient descent method for MOP enjoys the same convergence properties as those for scalar optimization.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1808-m2017-0214

Journal of Computational Mathematics, Vol. 37 (2019), Iss. 5 : pp. 689–703

Published online:    2019-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    15

Keywords:    Multi-objective optimization Gradient descent Gradient descent Convergence rate.

Author Details

Liaoyuan Zeng

Yuhong Dai

Yakui Huang

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