Optimization and Equilibrium

Projected solutions of quasi-variational inequalities with application to bidding process in electricity market

Event Date: Jan 17, 2018 in Optimization and Equilibrium, Seminars

Abstract:   Quasi-variational inequalities provide perfect tools  to reformulate Generalized Nash Equilibrium Probem (GNEP), the latter being a good model to describe the day-ahead  electricity markets.   Our aim in this talk is to illustrate how some recent advances in the theory  of quasi-variational inequalities can influence the modeling of electricity market.   Talk based on: – D. Aussel, A. Sultana & V. Vetrivel, On the existence of projected solutions of quasi-variational inequalities and generalized Nash equilibrium problem, J. Optim. Th. Appl. 170 (2016),...

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Projected solutions for quasi-equilibrium problems.

Event Date: Dec 06, 2017 in Optimization and Equilibrium, Seminars

Abstract:   In 2016, Aussel, Sultana and Vetrivel introduced the concept of projected solutions for generalized Nash equilibrium problems (GNEPs)in the finite dimensional case. To show the existence  of such solutions they studied projected solutions for quasi-variational inequality problems. In a similar spirit, we introduce the concept of projected solution for quasi-equilibrium problems (QEPs). As a consequence of our main result we obtain an existence result for projected solutions of GNEPs, in infinite dimensional spaces.  

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Existence results for equilibrium problem

Event Date: Nov 08, 2017 in Optimization and Equilibrium, Seminars

Abstract:   In this paper, we introduce certain regularizations for bifunctions, based on the corresponding regularization for functions, originally defined by J-P. Crouzeix. We show that the equilibrium problems associated to a bifunction and its regularizations are equivalent in the sense that they share the same solution set. Also, we introduce new existence results for the Equilibrium Problem, and we show some applications to minimization and Nash equilibrium...

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Event Date: Nov 22, 2017 in Optimization and Equilibrium, Seminars

Expositores 16:00–16:30hrs  Prof. Boulmezaoud, Tahar Zamene, Laboratoire de Mathématiques de Versailles, Université de Versailles, France Title: On Fourier transform and weighted Sobolev spaces Astract: We prove that Fourier transform defines a simple correspondance between weighted Sobolev spaces. As a consequence, we display a chain of nested invariant spaces over which Fourier transform is an isometry. &&&&& 16:30–17:00 hrs Prof. Lev Birbrair, Federal Univerisity of Ceara, Brazil Title: Resonance sequences.  Differential equations meet Number Theory....

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Limits of sequences of maximal monotone operators.

Event Date: Nov 15, 2017 in Optimization and Equilibrium, Seminars

Abstract: We consider a sequence of maximal monotone operators on a reflexive Banach space. In general, the (Kuratowski) lower limit of such a sequence is not a maximal monotone operator. So, what can be said? In the first part of the talk, we show that such a limit is a representable monotone operator while its Mosco limit, when it exists, is a maximal monotone operator. As an application of the former result, we obtain that the variational sum of two maximal monotone operators is a representable monotone operator. In the second part of the talk, we consider a sequence  of representative...

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An adverse selection approach to power pricing

Event Date: Aug 02, 2017 in Optimization and Equilibrium, Seminars

Abstract: We study the optimal design of electricity contracts among a  population of consumers with different needs. This question is tackled within the framework of Principal-Agent  problem in presence of adverse selection. The particular features of electricity induce an unusual  structure on the production cost, with no decreasing return to scale. We are nevertheless able to provide an  explicit solution for the problem at hand.  The optimal contracts are either linear or polynomial with  respect to the consumption. Whenever the outside options offered by competitors are not uniform...

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