## 3 SESIONES SEMINARIO OPTIMIZACION Y EQUILIBRIO

EXPOSITORES 16:00–16:30 hrs. Prof. Boulmezaoud, Tahar Zamene, Laboratoire de Mathématiques de Versailles, Université de Versailles, France Title: TBA 16:30–17:00 hrs. Prof. Lev Birbrair, Federal Univerisity of Ceara, Brazil Title: Resonance sequences. Differential equations meet Number Theory. Abstract: We will present some combinatorial or number theoretical problems coming from Geometric Theory of Ordinary Differential Equations of the Second Order. 17:00—17:10 hrs. Coffee Break 17:10–17:40 hrs, Prof. Huynh Van Ngai, University of Quy Nhon, Vietnam Title: Inverse...

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...

Read More## An adverse selection approach to power pricing

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...

Read More## Stability of Hamiltonian systems which are close to integrable : introduction to KAM and Nekhoroshev theory

Abstract: We give a panorama of classical theories of stability of Hamiltonian systems close to integrable which are of two kind : – Stability in measure over infinite time (KAM theory). – Effective stability over finite but very long time (Nekhoroshev theory)

Read More## Provably efficient high dimensional feature extraction

Abstract: The goal of inference is to extract information from data. A basic building block in high dimensional inference is feature extraction, that is, to compute functionals of given data that represent it in a way that highlights some underlying structure. For example, Principal Component Analysis is an algorithm that finds a basis to represent data that highlights the property of data being close to a low-dimensional subspace. A fundamental challenge in high dimensional inference is the design of algorithms that are provably efficient and accurate as the dimension grows. In this...

Read More## Iterative regularization via a dual diagonal descent method

Abstract: In the context of linear inverse problems, we propose and study general iterative regularization method allowing to consider classes of regularizers and data-fit terms. The algorithm we propose is based on a primal-dual diagonal descent method, designed to solve hierarchical optimization problems. Our analysis establishes convergence as well as stability results, in presence of error in the data. In this noisy case, the number of iterations is shown to act as a regularization parameter, which makes our algorithm an iterative regularization...

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