非负正交约束优化问题的理论、算法及应用

doi:10.15960/j.cnki.issn.1007-6093.2023.04.007

摘要/Abstract

摘要：

非负正交约束优化问题是同时带有非负约束和正交约束的优化问题, 该类问题在机器学习和数据科学中有着重要的应用。常见的非负正交约束优化问题包括二次指派问题、图匹配问题、非负正交矩阵分解问题、非负主成分分析和K-指示模型等。由于非负约束和正交约束的共同作用, 该类问题具有一定的组合结构, 一般是NP-难的。本文主要介绍非负正交约束优化问题的基本理论性质、求解算法以及相关的应用模型。

关键词: 非负正交约束优化, 置换矩阵约束优化, 精确罚函数, ?_p正则化, 二次指派问题

Abstract:

Optimization with nonnegative orthogonality constraints, which includes both nonnegative constraints and orthogonality constraints, has important applications in machine learning and data science. Some typical instances of optimization with nonnegative orthogonality constraints include the quadratic assignment problem, graph matching problem, orthogonal nonnegative matrix factorization problem, nonnegative principal component analysis, and K-indicator model, etc. Due to the coupling effects of nonnegative and orthogonal constraints, this type of problem has a certain combinatorial structure and is generally NP-hard. This paper mainly introduces the basic theoretical properties, algorithms, and related applications of optimization with nonnegative orthogonality constraints.

Key words: optimization with nonnegative orthogonality constraints, optimization with permutation matrices constraints, exact penalty, ?_p regularization, quadratic assignment problem

中图分类号:

O221.2

姜波. 非负正交约束优化问题的理论、算法及应用[J]. 运筹学学报, 2023, 27(4): 136-152.

Bo JIANG. On the theories, algorithms, and applications of optimization with nonnegative orthogonality constraints[J]. Operations Research Transactions, 2023, 27(4): 136-152.

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