Conic Mixed-Binary Sets: Convex Hull Characterizations and Applications

A Unifying Framework for the Convexification of Mixed-Integer Conic Binary Sets The paper “Conic Mixed-Binary Sets: Convex Hull Characterizations and Applications,” by Fatma Kilinc-Karzan, Simge Kucukyavuz, Dabeen Lee, and Soroosh Shafieezadeh-Abadeh, develops a unifying framework for convexifying mixed-integer conic binary sets. Many applications in machine-learning and operations research give rise to integer programming models with nonlinear structures and binary variables. The paper develops general methods for generating strong valid inequalities that take into account multiple conic constraints at the same time. The authors demonstrate that their framework applies to conic quadratic programming with binary variables, fractional programming, best subset selection, distributionally robust optimization, and sparse approximation of positive semidefinite matrices.