Well-posedness and global error bound for generalized mixed quasi-variational-hemivariational inequalities via regularized gap functions

• Published in: Optimization Vol. ahead-of-print; no. ahead-of-print; pp. 1 - 23
• Main Authors: Van Hung, Nguyen, Li, Lijie, Migórski, Stanislaw, Tam, Vo Minh
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 26.07.2023
• Subjects: error bound; Generalized mixed quasi-variational-hemivariational inequality; Levitin-Polyak well-posedness; quasi-optimization problem; regularized gap function
• ISSN: 0233-1934; 1029-4945
• DOI: 10.1080/02331934.2023.2239839

The aim of this paper is to establish new results on a class of generalized mixed quasi-variational-hemivariational inequalities (GMQVHVI, for short) via regularized gap functions. First, we introduce the new regularized gap function of GMQVHVI. Then we establish the criterion of the Levitin-Polyak well-posedness for GMQVHVI under suitable conditions. Further, we provide the equivalence between the Levitin-Polyak well-posedness in the generalized sense for GMQVHVI and that for a quasi-optimization problem using the new regularized gap function. Finally, the global error bound for GMQVHVI in term of the regularized gap function is derived by employing some the properties of the Clarke generalized directional derivative and strong monotonicity conditions.