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.
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