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Nonlinear Programming Techniques for Equilibria

  • Giancarlo Bigi
  • Marco Castellani
  • Massimo Pappalardo
  • Mauro Passacantando

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

Table of contents

  1. Front Matter
    Pages i-viii
  2. Giancarlo Bigi, Marco Castellani, Massimo Pappalardo, Mauro Passacantando
    Pages 1-16
  3. Giancarlo Bigi, Marco Castellani, Massimo Pappalardo, Mauro Passacantando
    Pages 17-50
  4. Giancarlo Bigi, Marco Castellani, Massimo Pappalardo, Mauro Passacantando
    Pages 51-71
  5. Giancarlo Bigi, Marco Castellani, Massimo Pappalardo, Mauro Passacantando
    Pages 73-97
  6. Back Matter
    Pages 99-120

About this book

Introduction

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. 

Keywords

variational inequalities complementarity multiobjective optimization fixed point problems noncooperative games inverse optimization convex optimization nonsmooth calculus Lagrangian duality Ky Fan inequalities

Authors and affiliations

  • Giancarlo Bigi
    • 1
  • Marco Castellani
    • 2
  • Massimo Pappalardo
    • 3
  • Mauro Passacantando
    • 4
  1. 1.Department of Computer ScienceUniversity of PisaPisaItaly
  2. 2.Department of Information Engineering, Computer Science and MathematicsUniversity of L’AquilaL’AquilaItaly
  3. 3.Department of Computer ScienceUniversity of PisaPisaItaly
  4. 4.Department of Computer ScienceUniversity of PisaPisaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-00205-3
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Business and Management
  • Print ISBN 978-3-030-00204-6
  • Online ISBN 978-3-030-00205-3
  • Series Print ISSN 2364-687X
  • Series Online ISSN 2364-6888
  • Buy this book on publisher's site
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