Sensitivity analysis for weak and strong vector quasiequilibrium problems (Q1030960)

The paper of Lam Quoc Anh and Phan Quoc Khanh is located in the area of the solution of systems of equations and inequalities, the latter ones understood with respect to different orderings. The solution sets are studied under parametrical variation and in view of their local and global structure, with a special interest in stability, represented in terms of various (generalized) continuity kind of conditions. Motivations for such studies can be derived from optimization theory and optimal control theory: the investigation of constraint qualifications (e.g., of MFCQ kind) and their topological-geometrical meaning, from the theory of bilevel problems and the theory of variational inequalities, from geometry and special topics of dynamical systems theory and game theory. Since the paper's setting is very general, namely due to the consideration of topological spaces and topological vector spaces, and a rich functional and parametrical setting is provided, possible meanings and applications could go much beyond these motivations and, in fact, wait to be discovered and used. The authors present the main contributions of their recent works on various kinds of stability for vector quasiequilibrium problems. They reflect the major results and are improvements or modifications, not repeated statements, of the authors' recent sufficient conditions for semicontinuities, continuity and Hölder continuity of solution maps of the considered problems. This article is well written and structured, it advances theory and could serve to support future research and practical applications as well. It consists of Section 1 (introduction), Section 2 on semicontinuities of solution maps, Section 3 on continuities of solution maps, Section 4 on Hölder continuity of solution maps, and of Section 5 on particular cases. Future real-world interpretations, verification of abstract topological and continuity conditions by characterizing (e.g., differential of algebraical) conditions, and practical application may be found and could become useful in connection with other sciences, with engineering, OR or economics.