Generalized Nash Equilibrium Problems, Bilevel Programming and MPEC

Deals with three frontiers in applied mathematics: generalized Nash equilibrium problems, bi-level programming, and mathematical programs with equilibrium constants (MPECs), with equilibrium being the central theme

Discusses both the variational techniques and the applications to economy, thereby catering to theorists and practitioners alike

Presents geometrical and numerical illustrations, suitable examples and exercises to promote a clearer understanding of the concept

Discusses applications of variational techniques in the electricity market

Includes contributions by eminent researchers in the field from across the world

Auteur

D. AUSSEL is a Professor at the Department of Mathematics and Computer Science, University of Perpignan, France. He is an expert on the theoretical aspects of quasi-convex optimization and variational inequalities. In addition, his research also involves applications of optimization in engineering processes and mathematical economics, in particular for the modeling of electricity markets, a topic where Nash equilibrium and multi-leader-follower games play a central role. He has published over 50 research articles in several prominent mathematics journals such as Transactions of the American Mathematical Society, SIAM Journal on Control and Optimization, Journal of Optimization Theory and Applications, as well as physics journals including Energy Conversion and Management. He is an associate editor of the journal Optimization and has served nearly a decade as the Co-Director and subsequently as Director of the French CNRS Research Group on Mathematics of Optimization and Applications. He has supervised several Ph.D. students, mainly on topics concerning nonsmooth variational analysis and electricity markets. Deeply interested in conveying research knowledge to young generations, he has been actively involved in the organization of research schools and research courses all over the world, including countries such as Vietnam, India, Chile, Peru, Cuba, Taiwan and Saudi Arabia.

C.S. LALITHA is a Professor at the Department of Mathematics, University of Delhi, South Campus, New Delhi, India. Her areas of interest include optimization theory, nonsmooth analysis and variational inequalities. She has co-authored more than 50 research papers published in prominent journals such as Journal of Optimization Theory and Applications, Optimization, Optimization Letters, Journal of Global Optimization, and Journal of Mathematical Analysis and Applications. She has also co-authored a book entitled Generalized Convexity, Nonsmooth Inequalities and Nonsmooth Optimization and has co-edited a book Combinatorial Optimization: Some Aspects, published by Narosa. She is a recipient of the INSA Teacher Award 2016. She has supervised many MPhil and Ph.D. students at the University of Delhi and is a member of various learned scientific societies such as the American Mathematical Society, the Operational Research Society of India, the Indian Mathematical Society and the Ramanujan Mathematical Society. She has organized many training programs, seminars and conferences. In addition, she has presented papers and delivered talks at several national and international conferences and workshops.

Contenu
Chapter 1. Bilevel Optimization: Reformulation and First Optimality Conditions.- Chapter 2. Calmness as a Constraint Qualification for M-Stationarity Conditions in MPECs.- Chapter 3. Optimality Conditions for Bilevel Programming: An Approach Through Variational Analysis.- Chapter 4. Mechanism Design and Auctions for Electricity Network.- Chapter 5. Reflection Methods for Inverse Problems with Applications toProtein Conformation Determination.- Chapter 6. On Single-Valuedness of Quasimonotone Set-Valued Operators.