Inexact Adaptive Cubic Regularization Algorithms on Riemannian Manifolds and Application

2024/05/04 by Zaijun Li, Xiaoming Wang, Li, Z. Y. +1
Computer Science · Engineering · Mathematics · #53C20(Primary) #53C22(Secondary) #Advanced Mathematical Modeling in Engineering #Advanced Numerical Analysis Techniques #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2405.02588

openalex publication_date 2024/05/04 · openalex created_date 2024/05/08 · openalex updated_date 2026/07/28

Abstract

The adaptive cubic regularization algorithm employing the inexact gradient and Hessian is proposed on general Riemannian manifolds, together with the iteration complexity to get an approximate second-order optimality under certain assumptions on accuracies about the inexact gradient and Hessian. The algorithm extends the inexact adaptive cubic regularization algorithm under true gradient in [Math. Program., 184(1-2): 35-70, 2020] to more general cases even in Euclidean settings. As an application, the algorithm is applied to solve the joint diagonalization problem on the Stiefel manifold. Numerical experiments illustrate that the algorithm performs better than the inexact trust-region algorithm in [Advances of the neural information processing systems, 31, 2018].

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