# Spectrally Constrained Optimization

arXiv: https://arxiv.org/abs/2307.04069 · HTML: https://mlsanity.com/paper/2307.04069/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jul 2023.

## Built on by (most cited first, 1 of 1)

- [The Spectral Barycentre of a Set of Graphs with Community Structure](https://mlsanity.com/paper/2502.00038/) (2025)

## Abstract (arXiv)

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.