String-averaging incremental subgradient methods for constrained convex optimization problems
In this doctoral thesis, we propose new iterative methods for solving a class of convex optimization problems. In general, we consider problems in which the objective function is composed of a finite sum of convex functions and the set of constraints is, at least, convex and closed. The iterative me...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2017 |
| País: | Brasil |
| Institución: | Universidade de São Paulo (USP) |
| Repositorio: | Biblioteca Digital de Teses e Dissertações da USP |
| Idioma: | inglés |
| OAI Identifier: | oai:teses.usp.br:tde-14112017-150512 |
| Acceso en línea: | http://www.teses.usp.br/teses/disponiveis/55/55134/tde-14112017-150512/ |
| Access Level: | acceso abierto |
| Palabra clave: | Algoritmos de média das sequências Convex optimization Incremental subgradient methods Métodos de subgradientes incrementais Otimização convexa Otimização estocástica Stochastic optimization String-averaging algorithms |
| Sumario: | In this doctoral thesis, we propose new iterative methods for solving a class of convex optimization problems. In general, we consider problems in which the objective function is composed of a finite sum of convex functions and the set of constraints is, at least, convex and closed. The iterative methods we propose are basically designed through the combination of incremental subgradient methods and string-averaging algorithms. Furthermore, in order to obtain methods able to solve optimization problems with many constraints (and possibly in high dimensions), generally given by convex functions, our analysis includes an operator that calculates approximate projections onto the feasible set, instead of the Euclidean projection. This feature is employed in the two methods we propose; one deterministic and the other stochastic. A convergence analysis is proposed for both methods and numerical experiments are performed in order to verify their applicability, especially in large scale problems. |
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