2023/11/14 by Jiefeng Xu, Can Li, Xu, Jiefeng +3
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Elasticity and Material Modeling #FOS: Mathematics #Optimization and Control (math.OC) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2311.07895
openalex publication_date 2023/11/14 · openalex created_date 2023/11/16 · openalex updated_date 2026/07/28
In this paper, we propose a feasible conjugate gradient (FCG) method for calculating \mathcal B-eigenpairs of a symmetric tensor \mathcal A. The method is an extension of the well-known conjugate gradient method for unconstrained optimization problems to some curve constrained optimization problems. The proposed FCG method can find a \mathcal B-eigenpair of a symmetric tensor \mathcal A without the requirement that the orders of \mathcal A and \mathcal B are equal. We pay particular attention to the Polak-Ribíre-Polyak (PRP) type conjugate gradient method. We show that the FCG method with some Armijo-type line search is globally convergent. Our numerical experiments indicate the promising performance of the proposed method.