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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.

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Metadaten
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
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