ON REGULARIZATION AND ACTIVE-SET METHODS WITH COMPLEXITY FOR CONSTRAINED OPTIMIZATION

Autor(es)

Birgin, E. G. ^[1] ; Martinez, J. M. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Math & Stat, Dept Comp Sci, Rua Matao 1010, Cidade Univ, BR-05508090 Sao Paulo, SP - Brazil

^[2] Univ Estadual Campinas, Inst Math Stat & Sci Comp, Dept Appl Math, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: SIAM JOURNAL ON OPTIMIZATION; v. 28, n. 2, p. 1367-1395, 2018.
• Citações Web of Science: 2

Resumo

The main objective of this research is to introduce a practical method for smooth bound-constrained optimization that possesses worst-case evaluation complexity O(epsilon (3/2)) for finding an epsilon-approximate first-order stationary point when the Hessian of the objective function is Lipschitz continuous. As other well-established algorithms for optimization with box constraints, the algorithm proceeds visiting the different faces of the domain aiming to reduce the norm of an internal projected gradient and abandoning active constraints when no additional progress is expected in the current face. The introduced method emerges as a particular case of a method for minimization with linear constraints. Moreover, the linearly constrained minimization algorithm is an instance of a minimization algorithm with general constraints whose implementation may be unaffordable when the constraints are complicated. As a procedure for leaving faces, a different method is employed that may be regarded as an independent device for constrained optimization. Such an independent algorithm may be employed to solve linearly constrained optimization problems on its own, without relying on the active-set strategy. A careful implementation and numerical experiments show that the algorithm that combines active sets with leaving-face iterations is more effective than the independent algorithm on which leaving-face iterations are based, although both exhibit similar complexities O(epsilon (-3/2)). (AU)

• Processo FAPESP: 13/03447-6 - Estruturas combinatórias, otimização e algoritmos em Teoria da Computação
• Beneficiário: Carlos Eduardo Ferreira
• Linha de fomento: Auxílio à Pesquisa - Temático
• Processo FAPESP: 13/05475-7 - Métodos computacionais de otimização
• Beneficiário: Sandra Augusta Santos
• Linha de fomento: Auxílio à Pesquisa - Temático
• Processo FAPESP: 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria
• Beneficiário: José Alberto Cuminato
• Linha de fomento: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs
• Processo FAPESP: 14/18711-3 - Modelagem matemática de sistemas e decisões
• Beneficiário: José Mário Martinez Perez
• Linha de fomento: Auxílio à Pesquisa - Pesquisador Visitante - Internacional