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| Author(s): |
Antonio Carlos dos Santos
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São Paulo. |
| Institution: | Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) |
| Defense date: | 2009-05-29 |
| Examining board members: |
Paulo José da Silva e Silva;
Ernesto Julian Goldberg Birgin;
Fernanda Maria Pereira Raupp
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| Advisor: | Paulo José da Silva e Silva |
| Abstract | |
This work deals with multiplier methods to solve semidefinite convex programming problems and the analysis of their proprieties based on the proximal point method applied on the dual problem. We focus on a subclass of semidefinite programming problems with affine constraints, for which we study duality relations an conditions for the existence of solutions of the primal and dual problems. Afterwards, we analyze two multiplier methods to solve this class of problems which are extensions of known methods in nonlinear programming. The first one, introduced by Doljansky e Teboulle, approaches an entropic interior proximal algorithm and their relationship with an exponential multiplier method. The second one, presented by Mosheyev e Zibulevsky, extends a smooth augmented Lagrangian method proposed by Ben-Tal and Zibulevsky for the problems of our interest. Finally, we present the results of numerical experiments for the algorithm proposed by Mosheyev e Zibulevsky, analyzing some choices of parameters, the sparsity patterns of matrices of the problem and criteria to accept approximate solutions of the unconstrained subproblems that must be solved at each iteration of the augmented Lagrangian method. (AU) | |