Equilibrium Problems and Applications
Auteurs : Kassay Gábor, Rădulescu Vicențiu
Equilibrium Problems and Applications develops a unified variational approach to deal with single-valued, set-valued and quasi-equilibrium problems. The authors promote original results in relationship with classical contributions to the field of equilibrium problems. The content evolved in the general setting of topological vector spaces and it lies at the interplay between pure and applied nonlinear analysis, mathematical economics, and mathematical physics.
This abstract approach is based on tools from various fields, including set-valued analysis, variational and hemivariational inequalities, fixed point theory, and optimization. Applications include models from mathematical economics, Nash equilibrium of non-cooperative games, and Browder variational inclusions. The content is self-contained and the book is mainly addressed to researchers in mathematics, economics and mathematical physics as well as to graduate students in applied nonlinear analysis.
1. Preliminaries and basic mathematical tools2. An overview on equilibrium problems3. Mathematical tools for solving equilibrium problems4. Existence of solutions of equilibrium problems5. Well-posedness for the equilibrium problems6. Variational principles and variational analysis for the equilibrium problems7. Applications to sensitivity of parametric equilibrium problems8. Applications to Nash equilibrium9. Applications to mathematical economics10. Applications to variational inequalities and related topics11. Regularization and numerical methods for equilibrium problems
Primarily researchers in applied mathematics and econometrics, including graduate students in applied nonlinear analysis. A secondary audience includes researchers in mathematical physics. Upper level undergraduate students in applied mathematics may be interested
Vicen?iu D. Radulescu received his Ph.D. at the Université Pierre et Marie Curie (Paris 6) in 1995 under the supervision of Haim Brezis. In 2003 he defended his Habilitation Mémoire at the same university. Radulescu is Professor at the AGH University of Science and Technology in Kraków, Leading Senior Researcher at the Institute of Mathematics, Physics and Mechanics in Ljubljana, Professorial Fellow at the “Simion Stoilow Mathematics Institute of the Romanian Academy, and Professor at the University of Craiova. He is the author of about 300 research papers in nonlinear analysis and several books, including Variational and Nonvariational Methods in Nonlinear Analysis and Boundary Value Problems (Kluwer, 2003), Singular Elliptic Problems: Bifurcation and Asymptotic Analysis (Oxford University Press, 2008), Problems in Real Analysis: Advanced Calculus on the Real Axis (Springer, 2009), Variational Principles in Mathematical Physics, Geometry and Economics: Qualitative Analysis of Nonlinear Equations and Unilateral Problems (Cambridge University Press, 2010), Nonlinear PDEs: Mathematical Models in Biology, Chemistry and Population Ge
- A rigorous mathematical analysis of Nash equilibrium type problems, which play a central role to describe network traffic models, competition games or problems arising in experimental economics
- Develops generic models relevant to mathematical economics and quantitative modeling of game theory, aiding economists to understand vital material without having to wade through complex proofs
- Reveals a number of surprising interactions among various equilibria topics, enabling readers to identify a common and unified approach to analysing problem sets
- Illustrates the deep features shared by several types of nonlinear problems, encouraging readers to develop further this unifying approach from other viewpoints into economic models in turn
Date de parution : 10-2018
Ouvrage de 440 p.
15x22.8 cm
Thèmes d’Equilibrium Problems and Applications :
Mots-clés :
Approximate solution; Assistive technologies; Aubin property; Berge maximum theorem; Brouwer fixed point theorem; Browder variational inclusion; Continuous selection; Convex analysis; Ekeland's principle; Equilibrium problem; Fr�chet-Urysohn space; Human computer interactions; Kakutani fixed point theorem; KKM lemma; KKM mapping; Linear openness; Metric regularity; Michael selection theorem; Quasi lower semicontinuity; Quasi-equilibrium problem; Quasi-hemivariational inequality; Schauder fixed point theorem; Selection; Selection theory; Semicontinuity; Set-valued equilibrium problem; Set-valued mapping; Sperner lemma; Strong vector equilibrium problem; Sub-lower semicontinuous set-valued mapping; Sum of two bifunctions; System of equilibrium problems; User centred design; User involvement; User profile; Vector equilibrium problem; Weak vector equilibrium problem