Memory gradient method for multiobjective optimization

Chen, Wang; Yang, Xinmin; Zhao, Yong

doi:10.1016/j.amc.2022.127791

Cited by 2 publications

(2 citation statements)

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“…The objective function in (7) is proper, closed and strongly convex. Therefore, problem (7) admits a unique optimal solution, referred to as the steepest descent direction (see [12]).…”

Section: Preliminariesmentioning

confidence: 99%

“…To our knowledge, several strategies exist for choosing the search direction d k (see [3, 7, 8, 12-14, 22, 24, 33, 40] and references therein). A representative descent algorithm is the work of Fliege and Svaiter [12] in 2000, where t k satisfies the multi-objective Armijo rule and d k is generated by solving the strongly convex quadratic problem (see (7)) or its dual problem (see (10) and (11)). This results in the multi-objective steepest descent (MSD) method.…”

Section: Introductionmentioning

confidence: 99%

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Improvements to steepest descent method for multi-objective optimization

Chen,

Tang,

Yang

2024

Preprint

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In this paper, we propose an efficient strategy for improving the multi-objective steepest descent method proposed by Fliege and Svaiter (Math Methods Oper Res, 2000, 3: 479--494). The core idea behind this strategy involves incorporating a positive modification parameter into the iterative formulation of the multi-objective steepest descent algorithm in a multiplicative manner. This modification parameter captures certain second-order information associated with the objective functions. We provide two distinct methods for calculating this modification parameter, leading to the development of two improved multi-objective steepest descent algorithms tailored for solving multi-objective optimization problems. Under reasonable assumptions, we demonstrate the convergence of sequences generated by the first algorithm toward a critical point. Furthermore, for strongly convex multi-objective optimization problems, we establish the linear convergence to Pareto optimality of the sequence of generated points. The performance of the new algorithms is empirically evaluated through computational comparisons on a set of multi-objective test instances. The numerical results underscore that the proposed algorithms consistently outperform the original multi-objective steepest descent algorithm.

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“…The objective function in (7) is proper, closed and strongly convex. Therefore, problem (7) admits a unique optimal solution, referred to as the steepest descent direction (see [12]).…”

Section: Preliminariesmentioning

confidence: 99%