Regularized gap functions and error bounds for generalized mixed strong vector quasiequilibrium problems

• Published in: Computational & applied mathematics Vol. 37; no. 5; pp. 5935 - 5950
• Main Authors: Anh, Lam Quoc, Van Hung, Nguyen, Tam, Vo Minh
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01-11-2018; Springer Nature B.V
• Subjects: Applications of Mathematics; Applied physics; Computational mathematics; Computational Mathematics and Numerical Analysis; Continuity (mathematics); Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematics; Mathematics and Statistics; Regularization; 58E35; Strong vector quasiequilibrium; Strong monotonicity; 49J53; 90C25; 90C33; Error bounds; Regularized gap function; Scalarization methods
• ISSN: 0101-8205; 2238-3603; 1807-0302
• DOI: 10.1007/s40314-018-0670-y

In this paper, we consider generalized mixed strong vector quasiequilibrium problems in infinite-dimensional spaces. Using the nonlinear scalarization method, we first propose gap functions for such problems. Then, based on the Moreau–Yosida regularization of these functions, we introduce regularized gap functions for the reference problems. Next, we study sufficient conditions for the mentioned functions to be continuous. Finally, error bounds for the concerning problems in terms of regularized gap functions are investigated. Some examples are provided to illustrate our results.