Spectrally Constrained Optimization

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 ont...

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Bibliographic Details
Published in:Journal of scientific computing Vol. 100; no. 3; p. 89
Main Authors: Garner, Casey, Lerman, Gilad, Zhang, Shuzhong
Format: Journal Article
Language:English
Published: New York Springer US 01.09.2024
Springer Nature B.V
Subjects:
Algorithms
Computational Mathematics and Numerical Analysis
Constraints
Eigenvalues
First order algorithms
Investigations
Linear functions
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Matrices (mathematics)
Optimization
Theoretical
Eigenvalue optimization
68W40
90C52
Non-smooth analysis
65K10
90C26
Frank-Wolfe algorithm
Constrained optimization
Matrix completion
ISSN:0885-7474, 1573-7691
Online Access:Get full text
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Summary: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.
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-024-02636-9