| Texto completo | |
| Autor(es): |
Andreani, Roberto
;
Ramos, Alberto
;
Ribeiro, Ademir A.
;
Secchin, Leonardo D.
;
Velazco, Ariel R.
Número total de Autores: 5
|
| Tipo de documento: | Artigo Científico |
| Fonte: | IMA JOURNAL OF NUMERICAL ANALYSIS; v. 42, n. 2, p. 31-pg., 2021-04-27. |
| Resumo | |
Augmented Lagrangian (AL) algorithms are very popular and successful methods for solving constrained optimization problems. Recently, global convergence analysis of these methods has been dramatically improved by using the notion of sequential optimality conditions. Such conditions are necessary for optimality, regardless of the fulfillment of any constraint qualifications, and provide theoretical tools to justify stopping criteria of several numerical optimization methods. Here, we introduce a new sequential optimality condition stronger than previously stated in the literature. We show that a well-established safeguarded Powell-Hestenes-Rockafellar (PHR) AL algorithm generates points that satisfy the new condition under a Lojasiewicz-type assumption, improving and unifying all the previous convergence results. Furthermore, we introduce a new primal-dual AL method capable of achieving such points without the Lojasiewicz hypothesis. We then propose a hybrid method in which the new strategy acts to help the safeguarded PHR method when it tends to fail. We show by preliminary numerical tests that all the problems already successfully solved by the safeguarded PHR method remain unchanged, while others where the PHR method failed are now solved with an acceptable additional computational cost. (AU) | |
| Processo FAPESP: | 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria |
| Beneficiário: | Francisco Louzada Neto |
| Modalidade de apoio: | Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs |
| Processo FAPESP: | 13/05475-7 - Métodos computacionais de otimização |
| Beneficiário: | Sandra Augusta Santos |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |