Generalized well-posedness results for a class of new mixed variational inequalities. (1st February 2023)

• Record Type: Journal Article
• Authors: Cen, Jinxia; Min, Chao; Tang, Guo-ji; Thien Nguyen, Van
• Is Part Of: Optimization. Volume 72:Number 2(2023)
• Page Start: 411
• Page End: 437
• Publication Date: 2023-02-01
• Subjects: Mixed variational inequality -- generalized well-posedness -- approximating sequence -- perturbation -- convergence; 49J40 -- 47J20 -- 35J87 -- 49J53 -- 65Nxx; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1970752
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : This paper is devoted to investigate a generalized type of mixed variational inequality (GMVI) in Banach space. Under the general assumptions, we first apply Minty's approach to deliver an equivalent result for GMVI and provide the existence condition of the solutions of GMVI. Then, the concepts of the strong and the weak well-posedness are introduced in the generalized sense, which are applied to discuss the essential relation between the metric characterizations and the generalized strong well-posedness as well as the weak well-posedness for GMVI. Moreover, the theorems are established to determine the generalized the strong and the weak well-posedness of GMVI, respectively. Furthermore, we consider a family of approximating problems corresponding to GMVI, which are dominated by the perturbation parameter ε, and a critical convergence result is obtained. Finally, an example is given to illustrate our main results.