用于约束性多目标优化的远离步骤弗兰克-沃尔夫算法

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Computational Optimization and Applications Pub Date : 2024-05-07 DOI:10.1007/s10589-024-00577-5

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

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引用次数: 0

摘要

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。

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

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

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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来源期刊

Computational Optimization and Applications 数学-应用数学

CiteScore

3.70

自引率

9.10%

发文量

审稿时长

10 months

期刊介绍： Computational Optimization and Applications is a peer reviewed journal that is committed to timely publication of research and tutorial papers on the analysis and development of computational algorithms and modeling technology for optimization. Algorithms either for general classes of optimization problems or for more specific applied problems are of interest. Stochastic algorithms as well as deterministic algorithms will be considered. Papers that can provide both theoretical analysis, along with carefully designed computational experiments, are particularly welcome. Topics of interest include, but are not limited to the following: Large Scale Optimization, Unconstrained Optimization, Linear Programming, Quadratic Programming Complementarity Problems, and Variational Inequalities, Constrained Optimization, Nondifferentiable Optimization, Integer Programming, Combinatorial Optimization, Stochastic Optimization, Multiobjective Optimization, Network Optimization, Complexity Theory, Approximations and Error Analysis, Parametric Programming and Sensitivity Analysis, Parallel Computing, Distributed Computing, and Vector Processing, Software, Benchmarks, Numerical Experimentation and Comparisons, Modelling Languages and Systems for Optimization, Automatic Differentiation, Applications in Engineering, Finance, Optimal Control, Optimal Design, Operations Research, Transportation, Economics, Communications, Manufacturing, and Management Science.