Technical Note—Conic Mixed-Binary Sets: Convex Hull Characterizations and Applications

Fatma Kılınç-Karzan (), Simge Küçükyavuz (), Dabeen Lee () and Soroosh Shafieezadeh-Abadeh ()
Additional contact information
Fatma Kılınç-Karzan: Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
Simge Küçükyavuz: Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208
Dabeen Lee: Department of Industrial and Systems Engineering, KAIST, Daejeon 34141, South Korea
Soroosh Shafieezadeh-Abadeh: Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213

Operations Research, 2025, vol. 73, issue 1, 251-269

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 multiple general convex cone constraints instead of a single second-order cone type constraint. Second, it takes 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.

Keywords: Optimization; conic mixed-binary sets; conic quadratic optimization; convex hull; submodularity; fractional binary optimization; best subset selection (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://dx.doi.org/10.1287/opre.2020.0827 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:73:y:2025:i:1:p:251-269

Access Statistics for this article

More articles in Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().