## On regularization/convexification of functionals including an l2-misfit term

Abstract: A common technique for solving ill-posed inverse problems is to include some sparsity/low-rank constraint, and pose it as a convex optimization problem, as is done e.g. in compressive sensing. The corresponding functional to be minimized often includes an l2 data fidelity term plus a convex term forcing sparsity. However, for many applications a non-convex term would be more suitable, although this is usually discarded since it leads to issues with algorithm convergence, local minima etc. I will introduce a new transform to (partially) convexify non-convex functionals of the above...

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

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),...

Read More## Projected solutions for quasi-equilibrium problems.

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.

Read More## Existence results for equilibrium problem

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...

Read More## 3 SESIONES SEMINARIO OPTIMIZACION Y EQUILIBRIO

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....

Read More## Limits of sequences of maximal monotone operators.

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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