非凸多目标优化中一大类下降算法的收敛性和复杂性保证

IF 0.8 4区管理学 Q4 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Letters Pub Date : 2024-04-22 DOI:10.1016/j.orl.2024.107115

Matteo Lapucci

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引用次数: 0

摘要

我们探讨了非凸多目标优化中下降算法的全局收敛条件和最坏情况复杂度界限。具体来说，我们定义了最陡下降相关方向的概念。我们考虑沿着这些方向采取步骤的迭代算法，并根据标准的阿米约类型规则选择步长。我们证明，符合这一框架的方法自动享有全局收敛特性。此外，我们还证明，大多数已知算法都能满足的一个略微严格的属性，保证了与最陡降法相同的 O(ϵ-2) 复杂度约束。

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Convergence and complexity guarantees for a wide class of descent algorithms in nonconvex multi-objective optimization

We address conditions for global convergence and worst-case complexity bounds of descent algorithms in nonconvex multi-objective optimization. Specifically, we define the concept of steepest-descent-related directions. We consider iterative algorithms taking steps along such directions, selecting the stepsize according to a standard Armijo-type rule. We prove that methods fitting this framework automatically enjoy global convergence properties. Moreover, we show that a slightly stricter property, satisfied by most known algorithms, guarantees the same complexity bound of $O (ϵ^{- 2})$ as the steepest descent method.

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来源期刊

Operations Research Letters 管理科学-运筹学与管理科学

CiteScore

2.10

自引率

9.10%

发文量

111

审稿时长

83 days

期刊介绍： Operations Research Letters is committed to the rapid review and fast publication of short articles on all aspects of operations research and analytics. Apart from a limitation to eight journal pages, quality, originality, relevance and clarity are the only criteria for selecting the papers to be published. ORL covers the broad field of optimization, stochastic models and game theory. Specific areas of interest include networks, routing, location, queueing, scheduling, inventory, reliability, and financial engineering. We wish to explore interfaces with other fields such as life sciences and health care, artificial intelligence and machine learning, energy distribution, and computational social sciences and humanities. Our traditional strength is in methodology, including theory, modelling, algorithms and computational studies. We also welcome novel applications and concise literature reviews.