Approximation et résolution de problèmes d'équilibre, de point fixe et d'inclusion monotone

Abstract : This thesis is devoted to solving three basic types of problems which
arise in nonlinear hilbertian functional analysis and its applications: equilibrium problems for monotone bifunctions, fixed point problems for nonexpansive operators, and inclusion problems for monotone operators. Our aim is to devise new methods to approximate and construct solutions to these problems, and to study their asymptotic behavior. We first propose new viscous and visco-penalized perturbations for these problems and investigate the asymptotic behavior of the associated approximating curves as the perturbation vanishes. We then study the properties of discrete and continuous dynamical systems associated with these approximating curves. This investigation gives rise in particular to new algorithms, the convergence of which is established. Numerical applications to image restoration problems are provided to illustrate the implementation and the performance of some of the proposed algorithms.
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Sever Adrian Hirstoaga. Approximation et résolution de problèmes d'équilibre, de point fixe et d'inclusion monotone. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2006. Français. ⟨tel-00137228⟩

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