A second-order sequential optimality condition associated to the convergence of optimization algorithms

Autor(es)

Andreani, Roberto ^[1] ; Haeser, Gabriel ^[2] ; Ramos, Alberto ^{[2, 3]} ; Silva, Paulo J. S. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Dept Appl Math, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil

^[2] Univ Sao Paulo, Dept Appl Math, Rua Matao 1010 Cidade Univ, BR-05508090 Sao Paulo, SP - Brazil

^[3] Univ Fed Parana, Dept Math, Curitiba 19-081, BR-81531980 Curitiba, PR - Brazil

• Tipo de documento: Artigo Científico
• Fonte: IMA JOURNAL OF NUMERICAL ANALYSIS; v. 37, n. 4, p. 1902-1929, OCT 2017.
• Citações Web of Science: 8

Resumo

Sequential optimality conditions have recently played an important role on the analysis of the global convergence of optimization algorithms towards first-order stationary points, justifying their stopping criteria. In this article, we introduce a sequential optimality condition that takes into account second-order information and that allows us to improve the global convergence assumptions of several second-order algorithms, which is our main goal. We also present a companion constraint qualification that is less stringent than previous assumptions associated to the convergence of second-order methods, like the joint condition Mangasarian-Fromovitz and weak constant rank. Our condition is also weaker than the constant rank constraint qualification. This means that we can prove second-order global convergence of well-established algorithms even when the set of Lagrange multipliers is unbounded, which was a limitation of previous results based on Mangasarian-Fromovitz constraint qualification. We prove global convergence of well-known variations of the augmented Lagrangian and regularized sequential quadratic programming methods to second-order stationary points under this new weak constraint qualification. (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
• Processo FAPESP: 12/20339-0 - Métodos de penalidade, condições de otimalidade e aplicações
• Beneficiário: Paulo José da Silva e Silva
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 10/19720-5 - Condições de otimalidade e restauração inexata
• Beneficiário: Gabriel Haeser
• Modalidade de apoio: Auxílio à Pesquisa - Jovens Pesquisadores