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Nonlinear Programming Techniques for Equilibria

  • Textbook
  • © 2019

Overview

Authors:
  1. Giancarlo Bigi

    1. Department of Computer Science, University of Pisa, Pisa, Italy

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  2. Marco Castellani

    1. Department of Information Engineering, Computer Science and Mathematics, University of L’Aquila, L’Aquila, Italy

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  3. Massimo Pappalardo

    1. Department of Computer Science, University of Pisa, Pisa, Italy

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  4. Mauro Passacantando

    1. Department of Computer Science, University of Pisa, Pisa, Italy

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  • Presents a unified treatment of different mathematical models for equilibria
  • Provides a mathematically rigorous tutorial on Ky Fan inequalities
  • Focuses on diverse algorithmic schemes to better fit a wide range of applications

Part of the book series: EURO Advanced Tutorials on Operational Research (EUROATOR)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-viii
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  2. Equilibrium Models and Applications

    • Giancarlo Bigi, Marco Castellani, Massimo Pappalardo, Mauro Passacantando
    Pages 1-16

  3. Theory for Equilibria

    • Giancarlo Bigi, Marco Castellani, Massimo Pappalardo, Mauro Passacantando
    Pages 17-50

  4. Algorithms for Equilibria

    • Giancarlo Bigi, Marco Castellani, Massimo Pappalardo, Mauro Passacantando
    Pages 51-71

  5. Quasi-Equilibria

    • Giancarlo Bigi, Marco Castellani, Massimo Pappalardo, Mauro Passacantando
    Pages 73-97

  6. Back Matter

    Pages 99-120
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Computer Science, University of Pisa, Pisa, Italy

    Giancarlo Bigi, Massimo Pappalardo, Mauro Passacantando

  • Department of Information Engineering, Computer Science and Mathematics, University of L’Aquila, L’Aquila, Italy

    Marco Castellani

About the authors

Giancarlo Bigi got a Ph.D. in Mathematics from the University of Pisa, Italy. He is currently Associate Professor of Operations Research at the Department of Computer Science of the same university. He achieved the Italian National Habilitation for full professorship both in Operations Research and Mathematical Methods for Economics. He is currently serving on the Managing Board of EUROPT, the continuous optimization working group of EURO. His research interest are mainly about multiobjective and set-valued optimization, nonconvex programming, variational inequalities and other equilibrium problems including Ky Fan inequalities, game theory, and their applications. In particular, most of his recent work focuses on the existence and computation of solutions of Ky Fan inequalities. His research papers have been published in several scientific journals and volumes.


Marco Castellani is Full Professor of Mathematical Methods for Economics and Actuarial and Financial Sciences at the Department of Information Engineering, Computer Science and Mathematics of the University of L'Aquila, Italy. He received both his M.Sc. degree and his Ph.D. in Mathematics from the University of Pisa, Italy. He is author of more than forty scientific papers most of which published in international journals such as Journal of Mathematical Analysis and Applications, Nonlinear Analysis TMA, Journal of Convex Analysis, Journal of Optimization Theory and Applications, Journal of Global Analysis, European Journal of Operational Research, Operations Research Letters, Applied Mathematics and Optimization, Optimization Methods & Software. His research activities have been mainly focused on theoretical aspects of nonsmooth scalar and multiobjective optimization, variational and quasivariational inequalities, equilibrium problems. In particular, his most recent works concern the existence of both exact and approximate solutions ofKy Fan inequalities in infinite dimensional spaces, the study of their stability, the characterization of the solution sets.



Massimo Pappalardo is Full Professor of Operations Research at the Department of Computer Science of the University of Pisa, Italy. He received both his M.Sc. degree and his Ph.D. in Mathematics from the University of Pisa. He has been Director of the Department of Applied Mathematics of University of Pisa and he is actually dean of the master degree in Computer Science of the University of Pisa. He is author of more than sixty scientific papers most of which published in international journals such as Journal of Optimization Theory and Applications, Journal of Global Optimization, European Journal of Operational Research, Optimization, Operations Research Letters, Optimization Methods & Software,  Journal of Mathematical Analysis and Applications. He is associate editor of the Journal “Minimax theory and its Applications”. His research activities have been mainly focused on theory and methods of nonlinear scalar and multiobjective optimization, variational and quasivariational inequalities, equilibrium problems.



Mauro Passacantando is Assistant Professor of Operations Research at the Department of Computer Science of the University of Pisa, Italy. He received both his M.Sc. and Ph.D. in Mathematics from the University of Pisa. He is author of more than forty scientific papers most of which published in international journals such as Computational Optimization and Applications, European Journal of Operational Research, INFORMS Journal on Computing, IEEE Transactions on Services Computing, Journal of Global Optimization, Journal of Optimization Theory and Applications, Optimization Methods & Software. His research activities are mainly focused on variational inequalities, projected dynamical systems, equilibrium problems, and their applications. In particular, most of his recent work focuses on theory and algorithms for Ky Fan inequalities and on game theoretic approaches to service provisioning problems in cloud and multi-cloud systems.



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