Properties of the delayed weighted gradient method

Autor(es)

Andreani, Roberto ^[1] ; Raydan, Marcos ^[2]

Afiliação do(s) autor(es)

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

^[2] UNL, FCT, Ctr Matemat & Aplicacoes CMA, P-2829516 Caparica - Portugal

• Tipo de documento: Artigo Científico
• Fonte: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS; v. 78, n. 1, p. 167-180, JAN 2021.
• Citações Web of Science: 0

Resumo

The delayed weighted gradient method, recently introduced in Oviedo-Leon (Comput Optim Appl 74:729-746, 2019), is a low-cost gradient-type method that exhibits a surprisingly and perhaps unexpected fast convergence behavior that competes favorably with the well-known conjugate gradient method for the minimization of convex quadratic functions. In this work, we establish several orthogonality properties that add understanding to the practical behavior of the method, including its finite termination. We show that if the n x n real Hessian matrix of the quadratic function has only p < n distinct eigenvalues, then the method terminates in p iterations. We also establish an optimality condition, concerning the gradient norm, that motivates the future use of this novel scheme when low precision is required for the minimization of non-quadratic functions. (AU)

• 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: 13/05475-7 - Métodos computacionais de otimização
• Beneficiário: Sandra Augusta Santos
• Modalidade de apoio: Auxílio à Pesquisa - Temático