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矩阵优化扰动性分析的若干进展

丁超1,*   

  1. 1.中国科学院数学与系统科学研究院, 北京 100190
  • 收稿日期:2017-08-15 出版日期:2017-12-15 发布日期:2017-12-15
  • 通讯作者: 丁超 dingchao@amss.ac.cn
  • 基金资助:

    国家自然科学基金 (Nos. 11671387, 11301515)

Preemptive online algorithms for scheduling

DING　Chao1,*   

  1. 1.  Academy of Mathematics and Systems Science,  Chinese Academy of Sciences, Beijing 100190, China
  • Received:2017-08-15 Online:2017-12-15 Published:2017-12-15

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摘要：

由于近年来实际问题特别是大数据应用的发展, 矩阵优化问题越来越得到优化研究者, 甚至是其他领域的研究者的高度关注, 成为热点问题. 优化问题的扰动性分析是优化理论研究的基础与核心, 为包括算法设计在内的优化研究提供重要的理论基础. 由于矩阵优化问题的非多面体性, 使得相应扰动分析理论的研究本质上与经典的多面体优化问题(非线性规划)不同. 结合文献~[1,2], 简要介绍矩阵优化扰动性分析方面取得的若干最新进展.

关键词: 矩阵优化, 扰动性分析, 鲁棒孤立平稳性, 平稳性, 度量次正则

Abstract:

Matrix optimization problems (MOPs) have been recognized in recent years to be a powerful tool to model many important applications arising from emerging fields such as data science  {within and beyond the optimization community}. Perturbation analysis of optimization problems play a fundamental and crucial role in optimization, which provided important theoretical foundation for algorithm designing and others. Science MOPs are non-polyhedral, the corresponding analysis is totally different from that of the classical polyhedral case (e.g., the nonlinear programming). Basing on results obtained in [1,2], we summary the recent progress on perturbation analysis of MOPs.

Key words: matrix optimization, perturbation analysis, robustly isolated calmness, calmness, metric subregularity