Spectral-gauge cuts for semidefinite programming
Abstract
We use symmetric gauge theory to develop a general class of cutting-plane algorithms for semidefinite programming. We formulate a separation problem based on spectral normalizations induced by gauges and derive a closed-form separation oracle. This oracle yields an implementable cut-generation procedure that, by varying the gauge, recovers standard cut families and generates new ones with tunable spectral structure. We embed the oracle within Kelley's method and characterize convergence as a function of the chosen gauge and initial conic relaxation. Numerical experiments on small and large instances of box-constrained quadratic programming and sparse principal component analysis illustrate the versatility and performance of the proposed framework.
Cite
@article{arxiv.2607.05935,
title = {Spectral-gauge cuts for semidefinite programming},
author = {Antonio Sasaki and Sophie Demassey and Valentina Sessa},
journal= {arXiv preprint arXiv:2607.05935},
year = {2026}
}