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.

Bigi, G., Castellani, M., Pappalardo, M., Passacantando, M. (2019). Nonlinear programming techniques for equilibria. Springer [10.1007/978-3-030-00205-3].

Nonlinear programming techniques for equilibria

Passacantando, Mauro
2019

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.
No
Scientifica
Monografia o trattato scientifico - Monografia di Ricerca - Prima edizione
variational inequalities; complementarity; multiobjective optimization; fixed point problems; noncooperative games; inverse optimization; convex optimization; nonsmooth calculus; Lagrangian duality; Ky Fan inequalities
English
978-3-030-00204-6
https://link.springer.com/book/10.1007/978-3-030-00205-3
Bigi, G., Castellani, M., Pappalardo, M., Passacantando, M. (2019). Nonlinear programming techniques for equilibria. Springer [10.1007/978-3-030-00205-3].
Bigi, G; Castellani, M; Pappalardo, M; Passacantando, M
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/392094
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