2023/07/09 by Casey Garner, Gilad Lerman, Garner, Casey +3
Computer Science · Mathematics · #65K10 #68W40 #90C26 #90C52 #Advanced Optimization Algorithms Research #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Matrix Theory and Algorithms #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2307.04069
openalex publication_date 2023/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate how to solve smooth matrix optimization problems with general linear inequality constraints on the eigenvalues of a symmetric matrix. We present solution methods to obtain exact global minima for linear objective functions, i.e., F(X) = ⟨ C, X ⟩, and perform exact projections onto the eigenvalue constraint set. Two first-order algorithms are developed to obtain first-order stationary points for general non-convex objective functions. Both methods are proven to converge sublinearly when the constraint set is convex. Numerical experiments demonstrate the applicability of both the model and the methods.