多面体投影算子广义雅克比的高效计算及拓展

doi:10.15960/j.cnki.issn.1007-6093.2023.04.004

运筹学学报（中英文） ›› 2023, Vol. 27 ›› Issue (4): 61-80.doi: 10.15960/j.cnki.issn.1007-6093.2023.04.004

所属专题：第八届中国运筹学会科学技术奖获奖者专辑

多面体投影算子广义雅克比的高效计算及拓展

邓生翔¹, 郦旭东¹^,*()

1. 复旦大学大数据学院, 上海 200433

收稿日期:2023-05-02 出版日期:2023-12-15 发布日期:2023-12-07
通讯作者: 郦旭东 E-mail:lixudong@fudan.edu.cn
基金资助:
国家自然科学基金(12271107);国家自然科学基金(62141407);上海市科学技术委员会基础研究重点项目(21JC1400600)

Fast computation of generalized Jacobians of polyhedral projectors and extensions

Shengxiang DENG¹, Xudong LI¹^,*()

1. School of Data Science, Fudan University, Shanghai 200433, China

Received:2023-05-02 Online:2023-12-15 Published:2023-12-07
Contact: Xudong LI E-mail:lixudong@fudan.edu.cn
About author:郦旭东, E-mail: lixudong@fudan.edu.cn

摘要/Abstract

摘要：

多面体投影算子在现代优化中发挥着基础且重要的作用。近年来，多面体投影算子的广义雅可比的计算研究取得了重要进展。本文回顾了一些关于多面体投影和它们的广义雅可比的理论和计算发展。类似的分析也扩展到了强凸二次规划问题的解映射和连续分段仿射正则化函数的邻近映射。

关键词: 多面体投影, 广义雅可比, 非光滑分析

Abstract:

Polyhedral projectors play a fundamental role in modern optimization. Recently, significant progress has been made in the computation of generalized Jacobians of projectors over polyhedral convex sets. In this paper, we review some recent theoretical and computational developments related to polyhedral projectors and their generalized Jacobians. Similar analyses are also extended to solution mappings of strongly convex quadratic programming problems, and proximal mappings of continuous piecewise affine regularizers.

Key words: projection onto polyhedrons, generalized Jacobians, nonsmooth analysis

中图分类号:

O224

邓生翔, 郦旭东. 多面体投影算子广义雅克比的高效计算及拓展[J]. 运筹学学报（中英文）, 2023, 27(4): 61-80.

Shengxiang DENG, Xudong LI. Fast computation of generalized Jacobians of polyhedral projectors and extensions[J]. Operations Research Transactions, 2023, 27(4): 61-80.

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多面体投影算子广义雅克比的高效计算及拓展

Fast computation of generalized Jacobians of polyhedral projectors and extensions

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