This book is a systematic and comprehensive exposition of the state-of-the-art research results in the literature on equilibrium problems. The book describes the highest-level research and reflects a current picture of results in the literature on the three topics in a very central place of the general theory of equilibrium problems: existence, stability, and approximation, together with their particular cases, and numerous applications. It is intended to serve as both introductory and deep courses for graduate students; or as useful materials for researchers studying aspects of optimization and equilibrium problems or, more generally, working on inter-discipline such as mathematical economics, operations research and management, or even in various areas of science and technology. In providing profound knowledge of recent research, this book has advantages over existing recent books focused on equilibrium problems and variational relation problems and may also be suitable for readers preparing deep and comprehensive graduate courses.

Presents materials from the state-of-the-art results for graduate students in comprehensive exploration of equilibrium problems Explores the stability and approximation of equilibrium problems Offers valuable guidance for researchers to develop their own results on related topics

Autorentext

Lam Quoc Anh received his PhD from the University of Science, VNU-HCM, Ho Chi Minh City, Vietnam, in 2007, under the supervision of Phan Quoc Khanh. He is currently a Professor of Mathematics at Cantho University (Cantho City, Vietnam). Following MathSciNet, he has authored more than 77 research papers on optimization-related problems, variational analysis, and nonlinear analysis, which have collectively garnered 874 citations. Lam Quoc Anh has delivered numerous invited talks at international conferences and workshops. He has collaborated with more than 20 co-authors and researchers worldwide and currently leads an optimization research group at Cantho University. Since 2018, he has been a member of the Vietnam Mathematical Society, and since 2022, he has served on the Council of Mathematics of the National Foundation for Science and Technology Development (NAFOSTED) in Vietnam. To date, 10 of his PhD students have successfully earned their doctorates, while 5 others are currently under his supervision.

Phan Quoc Khanh received his PhD under the supervision of Stefan Rolewicz in 1978 and his Habilitation Doctor in 1988, both at the Institute of Mathematics, Polish Academy of Sciences. From 2003-2020, he was a Professor in Mathematics at the International University, VNU-HCM, Ho Chi Minh City, Vietnam (from 2003-2007, he was the Founder-President of this university) and, from 2021, he is a professor-high-ranked researcher at Ton Duc Thang University. He was an Adjunct Professor of the Federation University, Australia, for many years. Since 2013, he has been a fellow of The World Academy of Sciences (TWAS) for the advancement of science in developing countries. Following MathSciNet, he is the author of 144 research papers, which have collectively garnered 1935 citations, on optimization-related problems, variational analysis, and nonlinear analysis. He was a member of Vietnam State Council for Professorship in Mathematics (2000-2024), Vice President of Vietnam Mathematical Society (2008-2018), Vice President of the Council of Mathematics of the National Foundation for Science and Technology Development (NAFOSTED) of Vietnam (2009-2018), member of the Scientific Council of Vietnam Institute for Advanced Study in Mathematics-VIASM (2010-2014). 20 of his PhD students received their doctorates; 1 other is currently under his supervision. He is an associate editor of many prestigious international journals.

Nguyen Hong Quan received his PhD at the University of Science, VNU-HCM, Ho Chi Minh City, Vietnam, under the supervision of Phan Quoc Khanh in 2014, and currently is the Associate Dean of the Faculty of Foundation Studies at Posts and Telecommunications Institute of Technology Ho Chi Minh City Campus. Following MathSciNet, he has published 16 research articles, which have collectively garnered 160 citations, on aspects of optimization-related problems, fixed-point theory, and nonlinear analysis in prestigious international journals. He is an advisor to 7 master students and many undergraduate students. He has reviewed many papers for Journal of Optimization Theory and Applications, Journal of Global Optimization

Inhalt

1 Solution Existence for Scalar Equilibrium Problems.- 2 Existence of Solutions to Scalar Quasiequilibrium Problems.- 3 Solution Existence for Vector Equilibrium Problems.- 4 Stability of Scalar Equilibrium Problems.- 5 Stability of Scalar Quasiequilibrium Problems.- 6 Stability of Vector Equilibrium Problems.- 7 Variational Convergence of Bifunctions and Approximations of Equilibrium Problems.- 8 Approximations of Quasiequilibrium Problems.- 9 Approximations of Vector Quasiequilibrium Problems.- 10 Variational Inclusion Problems and Variational Relation Problems.