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arXiv · 2307.04069

Spectrally Constrained Optimization

Casey Garner·Gilad Lerman·Shuzhong Zhang
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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., $F(X) = \langle C, X \rangle$, 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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Casey Garner, Gilad Lerman, Shuzhong Zhang. 2023-07-09. Spectrally Constrained Optimization. https://doi.org/10.1007/s10915-024-02636-9

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