Spectral Projected Gradient Methods: Review and Perspectives

Autor(es)

Birgin, Ernesto G. ^[1] ; Martinez, Jose Mario ^[2] ; Raydan, Marcos ^[3]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Dept Comp Sci, Inst Math & Stat, BR-05508090 Sao Paulo - Brazil

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

^[3] Univ Simon Bolivar, Dept Comp Cient & Fis Estadist, Caracas 1080A - Venezuela

• Tipo de documento: Artigo de Revisão
• Fonte: JOURNAL OF STATISTICAL SOFTWARE; v. 60, n. 3 SEP 2014.
• Citações Web of Science: 42

Resumo

Over the last two decades, it has been observed that using the gradient vector as a search direction in large-scale optimization may lead to efficient algorithms. The effectiveness relies on choosing the step lengths according to novel ideas that are related to the spectrum of the underlying local Hessian rather than related to the standard decrease in the objective function. A review of these so-called spectral projected gradient methods for convex constrained optimization is presented. To illustrate the performance of these low-cost schemes, an optimization problem on the set of positive definite matrices is described. (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