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群零模正则化问题的等价Lipschitz优化模型

陈星文1,*  潘少华1   

  1. 1. 华南理工大学数学学院, 广州 510640
  • 收稿日期:2016-06-30 出版日期:2018-09-15 发布日期:2018-09-15
  • 通讯作者: 陈星文 E-mail: shhpan@scut.edu.cn
  • 基金资助:

    国家自然科学基金(No. 11571120), 广东省自然科学基金(No. 2015A030313214)

Equivalent Lipschitz optimization model for the group zero-norm regularized problem

CHEN Xingwen1,*  PAN Shaohua1   

  1. 1. School of Mathematics, South China University of Technology, Guangzhou 510640, China
  • Received:2016-06-30 Online:2018-09-15 Published:2018-09-15

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摘要：

针对群零模正则化问题, 从零模函数的变分刻画入手, 将其等价地表示为带有 互补约束的数学规划问题(简称MPCC问题), 然后证明将互补约束直接罚到MPCC的目标函数而得到的罚问题是MPCC问题的全局精确罚. 此精确罚问题的目标函数不仅在可行集上全局Lipschitz连续而且还具有满意的双线性结构, 为设计群零模正则化问题的序列凸松弛算法提供了满意的等价Lipschitz优化模型.

关键词: 群零模正则化问题, MPCC 问题, 全局精确罚

Abstract:

With the help of the variational characterization of the zero-norm function, we reformulate the group zero-norm regularized problem as a MPCC (mathematical program with a complementarity constraint) and show that the penalty problem, yielded by moving the complementarity constraint into the objective, is a global exact penalty of the MPCC problem itself. The objective function of the exact penalty problem is not only global Lipschitz continuous in the feasible set but also has the desired bilinear structure, thereby providing a favorable equivalent Lipschitz optimization model for designing sequential convex relaxation algorithms of the group zero-norm regularized problem.

Key words: group zero-norm regularized problems, MPCC, global exact penalty