Operations Research Transactions ›› 2023, Vol. 27 ›› Issue (4): 61-80.doi: 10.15960/j.cnki.issn.1007-6093.2023.04.004

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Fast computation of generalized Jacobians of polyhedral projectors and extensions

Shengxiang DENG1, Xudong LI1,*()   

  1. 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

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

CLC Number: