{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/conic-mixed-binary-sets-convex-hull","title":"Conic Mixed-Binary Sets: Convex Hull Characterizations and Applications","arxiv_id":"2012.14698","date":"2020-12-29","proceeding":null,"authors":["Fatma Kılınç-Karzan","Simge Küçükyavuz","Dabeen Lee","Soroosh Shafieezadeh-Abadeh"],"abstract":"We consider a general conic mixed-binary set where each homogeneous conic constraint $j$ involves an affine function of independent continuous variables and an epigraph variable associated with a nonnegative function, $f_j$, of common binary variables. Sets of this form naturally arise as substructures in a number of applications including mean-risk optimization, chance-constrained problems, portfolio optimization, lot-sizing and scheduling, fractional programming, variants of the best subset selection problem, a class of sparse semidefinite programs, and distributionally robust chance-constrained programs. We give a convex hull description of this set that relies on simultaneous characterization of the epigraphs of $f_j$'s, which is easy to do when all functions $f_j$'s are submodular. Our result unifies and generalizes an existing result in two important directions. First, it considers \\emph{multiple general convex cone} constraints instead of a single second-order cone type constraint. Second, it takes \\emph{arbitrary nonnegative functions} instead of a specific submodular function obtained from the square root of an affine function. We close by demonstrating the applicability of our results in the context of a number of problem classes.","url_abs":"https://arxiv.org/abs/2012.14698v4","url_pdf":"https://arxiv.org/pdf/2012.14698v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"conic-mixed-binary-sets-convex-hull","repo_url":"https://github.com/sorooshafiee/best_subset_selection","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}