AN OVERVIEW OF OPTIMIZATION MANIFOLDS AND THEIR APPLICATIONS IN EIGEN VALUE PROBLEMS
By
U. S. Negi and Sulochana
Department of mathematics H. N. B. Garhwal (A Central University), S.R.T.Campus Badshithaul, Tehri Garhwal, Uttarakhand India- 249199
Email: usnegi7@gmail.com, sulochanabhandari77@gmail.com
(Received: August 03, 2022; In format: August 08, 2022; Revised: May 21, 2024; Accepted: October 26, 2024)
DOI: https://doi.org/10.58250/jnanabha.2024.54201
Abstract
Sra and Hussein [19] have studied on Conic geometric optimization on the manifold of positive definite matrices. Also, Hu and Zatwen [8] have calculated on a brief introduction to manifold optimization and Negi and Bisht [13] have deliberate geometric modeling approach to the means of positive definite symmetric metrices. In this paper, the author premeditated an overview of Optimization manifolds and its applications used in the optimization manifold Technique for solving linear eigen values problems. Also, we have calculated the g-convexity condition in some matrices and some functions.
2020 Mathematical Sciences Classification: 49Q12, 15B48, 52A21, 52A05.
Keywords: Manifold Optimization, Positive Symmetric Matrix, Hermitian Matrix, gconvexity, Geodesic, Convex function, convex set.