{"ID":2847210,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.00452","arxiv_id":"2511.00452","title":"On the Convexification of a Class of Mixed-Integer Conic Sets","abstract":"We investigate mixed-integer second-order conic (SOC) sets with a nonlinear right-hand side in the SOC constraint, a structure frequently arising in mixed-integer quadratically constrained programming (MIQCP). Under mild assumptions, we show that the convex hull can be exactly described by replacing the right-hand side with its concave envelope. This characterization enables strong relaxations for MIQCPs via reformulations and cutting planes. Computational experiments on distributionally robust chance-constrained knapsack variants demonstrate the efficacy of our reformulation techniques.","short_abstract":"We investigate mixed-integer second-order conic (SOC) sets with a nonlinear right-hand side in the SOC constraint, a structure frequently arising in mixed-integer quadratically constrained programming (MIQCP). Under mild assumptions, we show that the convex hull can be exactly described by replacing the right-hand side...","url_abs":"https://arxiv.org/abs/2511.00452","url_pdf":"https://arxiv.org/pdf/2511.00452v1","authors":"[\"Guxin Du\",\"Rui Chen\",\"Linchuan Wei\"]","published":"2025-11-01T08:35:07Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}