tailieunhanh - A summary of mathematics doctoral thesis: Cotinuity of solution mappings for equilibrium problems

Objective of the research: Study objects of this thesis are optimization related problems such as quasiequilibrium problems, quasivariational inequalities of the Minty type and the Stampacchia type, bilevel equilibrium problems, variational inequality problems with equilibrium constraints, optimization problems with equilibrium constraints and traffic network problems with equilibrium doctoral thesis | A summary of mathematics doctoral thesis: Cotinuity of solution mappings for equilibrium problems MINISTRY OF EDUCATION AND TRAINING VINH UNIVERSITY NGUYEN VAN HUNG COTINUITY OF SOLUTION MAPPINGS FOR EQUILIBRIUM PROBLEMS Speciality: Mathematical Analysis Code: 9 46 01 02 A SUMMARY OF MATHEMATICS DOCTORAL THESIS NGHE AN - 2018 Work is completed at Vinh University Supervisors: 1. Assoc. Prof. Dr. Lam Quoc Anh 2. Assoc. Prof. Dr. Dinh Huy Hoang Reviewer 1: Reviewer 2: Reviewer 3: Thesis will be presented and defended at school - level thesis evaluating Council at Vinh University at h date month year Thesis can be found at: 1. Nguyen Thuc Hao Library and Information Center 2. Vietnam National Library 1 PREFACE 1 Rationale . Stability of solutions for optimization related problems, including semicontinu- ity, continuity, H¨older/Lipschitz continuity and differentiability properties of the solu- tion mappings to equilibrium and related problems is an important topic in optimiza- tion theory and applications. In recent decades, there have been many works dealing with stability conditions for optimization-related problems as optimization problems, vector variational inequality problems, vector quasiequilibrium problems, variational re- lation problems. In fact, differentiability of the solution mappings is a rather high level of regularity and is somehow close to the Lipschitz continuous property (due to the Rademacher theorem). However, to have a certain property of the solution mapping, usually the problem data needs to possess the same level of the corresponding property, and this assumption about the data is often not satisfied in practice. In addition, in a number of practical situations such as mathematical models for competitive economies, the semicontinuity of the solution mapping is enough for the efficient use of the .