An away-step Frank–Wolfe algorithm for constrained multiobjective optimization

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-07 DOI:10.1007/s10589-024-00577-5

Douglas S. Gonçalves, Max L. N. Gonçalves, Jefferson G. Melo

引用次数: 0

Abstract

In this paper, we propose and analyze an away-step Frank–Wolfe algorithm designed for solving multiobjective optimization problems over polytopes. We prove that each limit point of the sequence generated by the algorithm is a weak Pareto optimal solution. Furthermore, under additional conditions, we show linear convergence of the whole sequence to a Pareto optimal solution. Numerical examples illustrate a promising performance of the proposed algorithm in problems where the multiobjective Frank–Wolfe convergence rate is only sublinear.

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用于约束性多目标优化的远离步骤弗兰克-沃尔夫算法

在本文中，我们提出并分析了一种专为解决多边形上的多目标优化问题而设计的分步 Frank-Wolfe 算法。我们证明了该算法生成的序列的每个极限点都是弱帕累托最优解。此外，在附加条件下，我们还证明了整个序列对帕累托最优解的线性收敛性。数值示例表明，在多目标 Frank-Wolfe 收敛率仅为亚线性的问题中，所提出的算法表现出良好的性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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