Barzilai-Borwein Proximal Gradient Methods for Multiobjective Composite Optimization Problems with Improved Linear Convergence

2023/06/16 by Chen, Jian, Tang, Liping, Yang, Xinmin · 1 citation
#90C29 #90C30 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2306.09797

Abstract

When minimizing a multiobjective optimization problem (MOP) using multiobjective gradient descent methods, the imbalances among objective functions often decelerate the convergence. In response to this challenge, we propose two types of the Barzilai-Borwein proximal gradient method for multi-objective composite optimization problems (BBPGMO). We establish convergence rates for BBPGMO, demonstrating that it achieves rates of O((1)/(√(k))), O((1)/(k)), and O(r^k)(0

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• Proximal Gradient Methods for Unconstrained Set Optimization Problems with Set-Valued Maps of Finite Cardinality

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