非光滑凸优化的可行平滑加速投影梯度法

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

Operations Research Letters Pub Date : 2024-09-02 DOI:10.1016/j.orl.2024.107181

Akatsuki Nishioka , Yoshihiro Kanno

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引用次数: 0

摘要

对于某些非光滑凸优化问题，平滑加速梯度法比子梯度法的收敛速度更快。然而，涅斯捷罗夫外推法可能需要在不可行点上进行梯度计算，因此无法应用于某些结构优化问题。我们引入了一种每个变量都可行的平滑加速投影梯度法的变体。利用 Lyapunov 函数可以获得 O(k-1logk) 的收敛速率。我们对桁架结构的鲁棒顺应性优化进行了数值实验。

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A feasible smoothing accelerated projected gradient method for nonsmooth convex optimization

Smoothing accelerated gradient methods achieve faster convergence rates than that of the subgradient method for some nonsmooth convex optimization problems. However, Nesterov's extrapolation may require gradients at infeasible points, and thus they cannot be applied to some structural optimization problems. We introduce a variant of smoothing accelerated projected gradient methods where every variable is feasible. The $O (k^{- 1} \log k)$ convergence rate is obtained using the Lyapunov function. We conduct a numerical experiment on the robust compliance optimization of a truss structure.

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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.