群零模正则化问题的等价Lipschitz优化模型

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

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.

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.