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| Author(s): |
Luiz Antonio da Silva Medeiros
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
| Defense date: | 2008-08-10 |
| Examining board members: |
Francisco de Assis Magalhães Gomes Neto;
Márcia Aparecida Gomes Ruggiero;
Maria de Los Angeles Gonzalez Lima;
Sandra Augusta Santos;
Ernesto Julián Goldberg Birgin
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| Advisor: | Francisco de Assis Magalhães Gomes Neto; José Mario Martínez Pérez |
| Abstract | |
In this work, we present an active set algorithm for minimizing the sum of squares of smooth functions, with box constraints. The algorithm is highly inspired in the work of Birgin and Mart'inez [4]. The differences are concentrated on the chosen search direction and on the use of an acceleration technique to update the step. At each iteration, we define an active face and solve an unconstrained quadratic subproblem using the Levenberg-Marquardt method (see [26], [28] and [33]), obtaining a descent direction and an approximate solution x+. Using only the free variables, we try to accelerate the method defining a new solution xa as a linear combination of the last p-1 approximate solutions together with x+. The coefficients of this linear combination are conveniently computed solving a constrained least squares problem that takes into account the objective function values of these p approximate solutions. Like in [4], we compute a line search and use projection techniques to add new constraints to the active set. The spectral projected gradient [5] is used to leave the current active face. Numerical experiments confirm that the algorithm is both efficient and robust. (AU) | |