We focus in this thesis, on splitting methods which be applied to special optimization or inclusion problems considering its related inclusion problems with an appropriated Lagrangian map. In a general setting for solving a monotone inclusion problem and obtain splitting algorithms, we develop a generalized proximal point and construct a related map with similar contraction properties as the resolvent map. Our general setting includes popular splitting algorithms. Also, we show decomposition techniques in order to solve the multi-block version of our model problems, _nding adequate formulations of the original problem and then apply a particular algorithm version of our general scheme. Finally, we apply the splitting method to a large-scale energy production planning problem.

En este trabajo desarrollamos una variante Relative-error e Inertial - Relaxed de los Métodos Punto Proximal y Punto Fijo, para luego, aprovechando la relación que poseen ciertos algoritmos de separación con los Métodos antes mencionados, aplicar estos métodos más generales para la obtención de las variantes del mismo tipo en esa clase de algoritmos de separación, los cuales permiten su aceleración y/o fácil implementación.