Nonlinear Programming Techniques for Equilibria

This book considers a range of problems in operations research, which are formulated through various mathematical models such as complementarity, variational inequalities, multiobjective optimization, fixed point problems, noncooperative games and inverse optimization. Moreover, the book subsumes all these models under a common structure that allows them to be formulated in a unique format: the Ky Fan inequality. It subsequently focuses on this unifying equilibrium format, providing a comprehensive overview of the main theoretical results and solution algorithms, together with a wealth of applications and numerical examples. Particular emphasis is placed on the role of nonlinear optimization techniques – e.g. convex optimization, nonsmooth calculus, proximal point and descent algorithms – as valuable tools for analyzing and solving Ky Fan inequalities. . Read more... Abstract: This book considers a range of problems in operations research, which are formulated through various mathematical models such as complementarity, variational inequalities, multiobjective optimization, fixed point problems, noncooperative games and inverse optimization. Moreover, the book subsumes all these models under a common structure that allows them to be formulated in a unique format: the Ky Fan inequality. It subsequently focuses on this unifying equilibrium format, providing a comprehensive overview of the main theoretical results and solution algorithms, together with a wealth of applications and numerical examples. Particular emphasis is placed on the role of nonlinear optimization techniques – e.g. convex optimization, nonsmooth calculus, proximal point and descent algorithms – as valuable tools for analyzing and solving Ky Fan inequalities Front Matter ....Pages i-viii Equilibrium Models and Applications (Giancarlo Bigi, Marco Castellani, Massimo Pappalardo, Mauro Passacantando)....Pages 1-16 Theory for Equilibria (Giancarlo Bigi, Marco Castellani, Massimo Pappalardo, Mauro Passacantando)....Pages 17-50 Algorithms for Equilibria (Giancarlo Bigi, Marco Castellani, Massimo Pappalardo, Mauro Passacantando)....Pages 51-71 Quasi-Equilibria (Giancarlo Bigi, Marco Castellani, Massimo Pappalardo, Mauro Passacantando)....Pages 73-97 Back Matter ....Pages 99-120