一种新的半有限优化内部点算法的复杂性分析与数值实现

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

Operations Research Letters Pub Date : 2024-09-27 DOI:10.1016/j.orl.2024.107192

Billel Zaoui, Djamel Benterki, Samia Khelladi

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引用次数: 0

摘要

我们将 Zhang 和 Xu（2011）[22] 的线性优化内部点算法推广到半有限优化问题中，以定义新的搜索方向。搜索方向的对称性基于完整的 Nesterov-Todd 缩放方案。此外，我们还证明了所获得的算法能在多项式时间内解决所研究的问题，而且短步算法具有已知的最佳迭代约束，即 O(nlognε)-iterations 。最后，我们报告了一项数值对比研究，以显示我们提出的算法的效率。

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Complexity analysis and numerical implementation of a new interior-point algorithm for semidefinite optimization

We generalize Zhang and Xu's (2011) [22] interior point algorithm for linear optimization to semidefinite optimization problems in order to define a new search direction. The symmetrization of the search direction is based on the full Nesterov-Todd scaling scheme. Moreover, we show that the obtained algorithm solves the studied problem in polynomial time and that the short-step algorithm has the best-known iteration bound, namely

O (\sqrt{n} \log \frac{n}{ε})

-iterations. Finally, we report a comparative numerical study to show the efficiency of our proposed algorithm.

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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.