Spectrally Constrained Optimization

Abstract

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.

arXiv comment32 pages, 2 figures, 2 tables

References in corpus (6)

• Robust Subspace Learning: Robust PCA, Robust Subspace Tracking, and Robust Subspace Recovery
• Global Optimality in Low-rank Matrix Optimization
• An Overview of Robust Subspace Recovery
• Numerical Optimization of Eigenvalues of Hermitian Matrix Functions
• On Generalizing Trace Minimization
• Eigenvalue programming beyond matrices

Cited by in corpus (1)

• Eigenvalue programming beyond matrices