Local optimality for stationary points of group zero-norm regularized problems and equivalent surrogates

Abstract

This paper focuses on the local optimality for the stationary points of the composite group zero-norm regularized problem and its equivalent surrogates. First, by using the structure of the composite group zero-norm and its second subderivative characterization, we achieve several local optimal conditions for a stationary point of the group zero-norm regularized problem. Then, we obtain a family of equivalent surrogates for the group zero-norm regularized problem from a class of global exact penalties of its MPEC reformulation, established under the calmness of a partial perturbation to the composite group zero-norm constraint system. For the stationary points of these surrogates, we study their local optimality to the surrogates themselves and the group zero-norm regularized problem. The local optimality conditions obtained in this work not only recover the existing ones for zero-norm regularized problems, but also provide new criteria to judge the local optimality of a stationary point yielded by an algorithm for solving the corresponding surrogate problems.

Keywords:

• Group zero-norm
• equivalent surrogates
• stationary points
• local optimality

2020 Mathematics Subject Classifications:

• 49J52
• 49J53
• 90C26

Acknowledgements

The authors would like to express their sincere thanks to the anonymous referee for his/her helpful comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [project No. 11971177] and Guangdong Basic and Applied Basic Research Foundation [2020A1515010408].