{"ID":2878727,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.18435","arxiv_id":"2508.18435","title":"A second-order cone representable class of nonconvex quadratic programs","abstract":"We consider the problem of minimizing a sparse nonconvex quadratic function over the unit hypercube. By developing an extension of the Reformulation-Linearization Technique (RLT) to continuous quadratic sets, we propose a novel second-order cone (SOC) representable relaxation for this problem. By exploiting the sparsity of the quadratic function, we establish a sufficient condition under which the convex hull of the feasible region of the lifted quadratic program is SOC-representable. While the proposed formulation may be of exponential size in general, we identify additional structural conditions that guarantee the existence of a polynomial-size SOC-representable formulation, which can be constructed in polynomial time. Under these conditions, the optimal value of the nonconvex quadratic program coincides with that of a polynomial-size second-order cone program. Our results serve as a starting point for bridging the gap between the Boolean quadric polytope of sparse problems and its continuous counterpart.","short_abstract":"We consider the problem of minimizing a sparse nonconvex quadratic function over the unit hypercube. By developing an extension of the Reformulation-Linearization Technique (RLT) to continuous quadratic sets, we propose a novel second-order cone (SOC) representable relaxation for this problem. By exploiting the sparsit...","url_abs":"https://arxiv.org/abs/2508.18435","url_pdf":"https://arxiv.org/pdf/2508.18435v2","authors":"[\"Santanu S. Dey\",\"Aida Khajavirad\"]","published":"2025-08-25T19:27:08Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}