Proximal decomposition method applied to energy planning problem with uncertainty

• Autor: Oré Albornoz, Ernesto
• Formato: tesis doctoral
• Fecha de Publicación: 2018
• Institución: Universidad Nacional de Ingeniería
• Repositorio: UNI-Tesis
• Lenguaje: inglés
• OAI Identifier: oai:cybertesis.uni.edu.pe:20.500.14076/26928
• Enlace del recurso: http://hdl.handle.net/20.500.14076/26928
• Nivel de acceso: acceso abierto
• Materia: Optimización matemática; Método de descomposición proximal; Planificación energética; https://purl.org/pe-repo/ocde/ford#1.01.02

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.