Spectral-gauge cuts for semidefinite programming

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.