{"ID":6023421,"CreatedAt":"2026-07-08T01:00:23.257252134Z","UpdatedAt":"2026-07-10T07:26:08.066495556Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.05935","arxiv_id":"2607.05935","title":"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.","short_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 varyin...","url_abs":"https://arxiv.org/abs/2607.05935","url_pdf":"https://arxiv.org/pdf/2607.05935v1","authors":"[\"Antonio Sasaki\",\"Sophie Demassey\",\"Valentina Sessa\"]","published":"2026-07-07T07:37:52Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.SP\"]","methods":"[]","has_code":false}