Stability analysis of split equality and split feasibility problems
- In this paper, for the first time in the literature, we study the stability of solutions of two classes of feasibility (i.e., split equality and split feasibility) problems by set-valued and variational analysis techniques. Our idea is to equivalently reformulate the feasibility problems as parametric generalized equations to which set-valued and variational analysis techniques apply. Sufficient conditions, as well as necessary conditions, for the Lipschitz-likeness of the involved solution maps are proved by exploiting special structures of the problems and by using an advanced result of B.S. Mordukhovich [J. Global Optim. 28, 347–362 (2004)]. These conditions stand on a solid interaction among all the input data by means of their dual counterparts, which are transposes of matrices and regular/limiting normal cones to sets. Several examples are presented to illustrate how the obtained results work in practice and also show that the assumption on the existence of a nonzero solution used in the necessity conditions cannot be lifted.
| Author: | Thi Huong VuORCiD, Hong-Kun XuORCiD, Dong Yen Nguyen |
|---|---|
| Document Type: | Article |
| Parent Title (English): | Journal of Global Optimization |
| Volume: | 92 |
| First Page: | 411 |
| Last Page: | 429 |
| Publisher: | Springer Science and Business Media LLC |
| Date of first Publication: | 2025/02/19 |
| ISSN: | 0925-5001 |
| DOI: | https://doi.org/10.1007/s10898-025-01469-6 |

