{"ID":2857805,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.09918","arxiv_id":"2510.09918","title":"Characterizing nonconvex boundaries via scalarization","abstract":"We present a unified approach for characterizing the boundary of a possibly nonconvex domain. Motivated by the well-known Pascoletti--Serafini method of scalarization, we recast the boundary characterization as a multi-criteria optimization problem with respect to a local partial order induced by a spherical cone with varying orient. Such an approach enables us to trace the whole boundary and can be considered a general dual representation for arbitrary (nonconvex) sets satisfying an exterior cone condition. We prove the equivalence between the geometrical boundary and the scalarization-implied boundary, particularly in the case of Euclidean spaces and two infinite-dimensional spaces for practical interest. By reformulating each scalarized problem as a parameterized constrained optimization problem, we shall develop a corresponding numerical scheme for the proposed approach. Some related applications are also discussed.","short_abstract":"We present a unified approach for characterizing the boundary of a possibly nonconvex domain. Motivated by the well-known Pascoletti--Serafini method of scalarization, we recast the boundary characterization as a multi-criteria optimization problem with respect to a local partial order induced by a spherical cone with...","url_abs":"https://arxiv.org/abs/2510.09918","url_pdf":"https://arxiv.org/pdf/2510.09918v1","authors":"[\"Jin Ma\",\"Weixuan Xia\",\"Jianfeng Zhang\"]","published":"2025-10-10T23:24:27Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.MG\"]","methods":"[]","has_code":false}