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Analyse et optimisation de problèmes sous contraintes d'autocorrélation

Abstract : In this work, we study how to take into account, from the convex analysis and optimization viewpoint, constraint sets of the following type : sets of vectors whose components are autocorrelations lags of finite discrete signals. A set of vectors with autocorrelated components turns out to be a convex cone, for which we etablish many basic properties such as : smoothness or not of the boundary, structure of faces, acuteness, expression of the polar cone, evaluation of the normal cone at a point, etc. Next, we propose some algorithms to solve optimization problems where this type of constraint set appears ; in particular we consider the problem of projecting a point on the convex cone of vectors with autocorrelated constraints. For these purposes, we study three different algorithms : an interior point method, one using alternating projections, and one via a non-convex relaxation of the original problem. Finally, we suggest extensions to the bi-dimensional signals case ; we outline the main difficulties which therefore appear : various possible new definitions, non-convexity of occuring problems, and increase in the computational complexity of the algorithmic procedures.
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https://tel.archives-ouvertes.fr/tel-00195013
Contributor : Marc Fuentes <>
Submitted on : Saturday, December 8, 2007 - 4:13:26 PM
Last modification on : Friday, October 23, 2020 - 4:42:46 PM
Long-term archiving on: : Monday, April 12, 2010 - 6:40:38 AM

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  • HAL Id : tel-00195013, version 1

Citation

Marc Fuentes. Analyse et optimisation de problèmes sous contraintes d'autocorrélation. Mathématiques [math]. Université Paul Sabatier - Toulouse III, 2007. Français. ⟨tel-00195013⟩

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