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CONSTRAINT QUALIFICATIONS AND STRONG GLOBAL CONVERGENCE PROPERTIES OF AN AUGMENTED LAGRANGIAN METHOD ON RIEMANNIAN MANIFOLDS

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Autor(es):
Andreani, Roberto ; Couto, Kelvin R. ; Ferreira, Orizon P. ; Haeser, Gabriel
Número total de Autores: 4
Tipo de documento: Artigo Científico
Fonte: SIAM JOURNAL ON OPTIMIZATION; v. 34, n. 2, p. 27-pg., 2024-01-01.
Resumo

In the past several years, augmented Lagrangian methods have been successfully applied to several classes of nonconvex optimization problems, inspiring new developments in both theory and practice. In this paper we bring most of these recent developments from nonlinear programming to the context of optimization on Riemannian manifolds, including equality and inequality constraints. Many research have been conducted on optimization problems on manifolds, however only recently the treatment of the constrained case has been considered. In this paper we propose to bridge this gap with respect to the most recent developments in nonlinear programming. In particular, we formulate several well-known constraint qualifications from the Euclidean context which are sufficient for guaranteeing global convergence of augmented Lagrangian methods, without requiring boundedness of the set of Lagrange multipliers. Convergence of the dual sequence can also be assured under a weak constraint qualification. The theory presented is based on so-called sequential optimality conditions, which is a powerful tool used in this context. The paper can also be read with the Euclidean context in mind, serving as a review of the most relevant constraint qualifications and global convergence theory of state-of-the-art augmented Lagrangian methods for nonlinear programming. (AU)

Processo FAPESP: 17/17840-2 - Estimativas de erro em otimização não linear
Beneficiário:Leonardo Makoto Mito
Modalidade de apoio: Bolsas no Brasil - Doutorado
Processo FAPESP: 23/08706-1 - Métodos computacionais de otimização
Beneficiário:Ernesto Julián Goldberg Birgin
Modalidade de apoio: Auxílio à Pesquisa - Temático
Processo FAPESP: 17/18308-2 - Condições de otimalidade e algoritmos de segunda-ordem
Beneficiário:Gabriel Haeser
Modalidade de apoio: Auxílio à Pesquisa - Regular
Processo FAPESP: 18/24293-0 - Métodos computacionais de otimização
Beneficiário:Sandra Augusta Santos
Modalidade de apoio: Auxílio à Pesquisa - Temático
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