Un Método de Gradiente Proyectado Espectral para el Problema de Mínimos Cuadrados Matricial Semi–definido Positivo

Translated title of the contribution: A Spectral Gradient Projection Method for the Positive Semi–definite Procrustes Problem

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Abstract

This paper addresses the positive semi-definite procrustes problem (PSDP). The PSDP corresponds to a least squares problem over the set of symmetric and semi-definite positive matrices. These kinds of problems appear in many applications such as structure analysis, signal processing, among others. A non-monotone spectral projected gradient algorithm is proposed to obtain a numerical solution for the PSDP. The proposed algorithm employs the Zhang and Hager’s non-monotone technique in combination with the Barzilai and Borwein’s step size to accelerate convergence. Some theoretical results are presented. Finally, numerical experiments are performed to demonstrate the effectiveness and efficiency of the proposed method, and comparisons are made with other state-of-the-art algorithms.

Translated title of the contributionA Spectral Gradient Projection Method for the Positive Semi–definite Procrustes Problem
Original languageSpanish
Pages (from-to)109-123
Number of pages15
JournalRevista Colombiana de Matematicas
Volume55
Issue number1
DOIs
StatePublished - 2021
Externally publishedYes

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