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| Author(s): |
Larissa Oliveira Xavier
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 Ciência da Computação |
| Defense date: | 2011-09-11 |
| Examining board members: |
Sandra Augusta Santos;
Márcia Aparecida Gomes Ruggiero;
Roberto Andreani;
Nelson Maculan Filho;
Ademir Alves Ribeiro
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| Advisor: | Sandra Augusta Santos; José Mario Martínez Pérez |
| Abstract | |
In this work two trust-region-based algorithms are analyzed for linearly constrained minimization. The first one is an active-set method, based on Gay's ideas. The second one uses interior-point techniques of barrier methods. Both algorithms are proved to be well defined and accompanied by the respective convergence results. The implementation was developed resting upon Rojas, Santos and Sorensen matrix-free algorithm for solving the inner trust-region subproblems. The family of adopted test-problems involves the distribution of points in a polygon, a modification of Powell's problem of distributing points in a square. Despite its favorable structure for generating instances with variable and potentially large dimension, in the matrix-free context, the problem is indeed hard and challenging, with many local minimizers. Comparative computational experiments illustrate the performance of the proposed algorithms, showing that both are effective to obtain second-order stationary points, with a slight advantage of the active-set-based algorithm when it comes to the CPU time spent (AU) | |
| FAPESP's process: | 06/04477-2 - On trust-region algorithms for linearly constrained minimization |
| Grantee: | Larissa Oliveira Xavier |
| Support Opportunities: | Scholarships in Brazil - Doctorate |