Optimization and Equilibrium

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

Event Date: Mar 29, 2017 in Optimization and Equilibrium, Seminars

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)

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Provably efficient high dimensional feature extraction

Event Date: Dec 28, 2016 in Optimization and Equilibrium, Seminars

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...

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Iterative regularization via a dual diagonal descent method

Event Date: Dec 14, 2016 in Optimization and Equilibrium, Seminars

   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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Does convexity arise in optimization naturally?

Event Date: Nov 16, 2016 in Optimization and Equilibrium, Seminars

Abstract Convexity is one of the conditions that any researcher may desire to have when dealing with problems in Optimization. Thus, the lack of standard convexity provides an interesting challenge in mathematics. In this talk we show various instances from mathematical programming, differential inclusions to calculus of variations, where convexity is present in one way or in another. Among the issues to be described lie: strong duality, KKT optimality conditions; joint-range and the S-lemma for a pair of (not necessarily homogeneous) quadratic functions; optimal value functions; local...

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The Schur property over some Lipschitz-free spaces.

Event Date: Oct 26, 2016 in Optimization and Equilibrium, Seminars

Abstract: Adjunto.

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On the Convergence of Projection Method for Co-coercive Variational Inequalities

Event Date: Oct 19, 2016 in Optimization and Equilibrium, Seminars

Abstract: We revisit the basic projection method for solving co-coercive  variational inequalities in real Hilbert spaces. The weak and the strong convergence for the  iterative sequences generated by this method are studied. We also propose several examples to analyze  the obtained results. This is a joint work with Phan Tu Vuong.

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