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.