固定维度下最小特征值最大化的快速算法

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

Operations Research Letters Pub Date : 2024-09-13 DOI:10.1016/j.orl.2024.107186

Adam Brown , Aditi Laddha , Mohit Singh

引用次数: 0

摘要

在最小特征值问题中，我们给定了 Rd 中的一系列向量，目标是选取一个子集 B，使矩阵∑i∈Bvivi⊤的最小特征值最大化。我们给出了一个 O(nO(dlog(d)/ϵ2))时间的随机算法，它能找到一个受分区约束的赋值，其最小特征值至少是最优值的 (1-ϵ) 倍，而且概率很高。作为副产品，我们还得到了卡迪森-辛格问题算法版本的一种简单算法。

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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Fast algorithms for maximizing the minimum eigenvalue in fixed dimension

In the minimum eigenvalue problem, we are given a collection of vectors in

R^{d}

, and the goal is to pick a subset B to maximize the minimum eigenvalue of the matrix

\sum_{i \in B} v_{i} v_{i}^{⊤}

. We give a

O (n^{O (d \log (d) / ϵ^{2})})

-time randomized algorithm that finds an assignment subject to a partition constraint whose minimum eigenvalue is at least

(1 - ϵ)

times the optimum, with high probability. As a byproduct, we also get a simple algorithm for an algorithmic version of Kadison-Singer problem.

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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.