Journal article
How to convexify the intersection of a second order cone and a nonconvex quadratic
Mathematical programming, Vol.162(1-2), pp.393-429
03/01/2017
DOI: 10.1007/s10107-016-1045-z
Abstract
A recent series of papers has examined the extension of disjunctive-programming techniques to mixed-integer second-order-cone programming. For example, it has been shown-by several authors using different techniques-that the convex hull of the intersection of an ellipsoid, , and a split disjunction, with , equals the intersection of with an additional second-order-cone representable (SOCr) set. In this paper, we study more general intersections of the form and , where is a SOCr cone, is a nonconvex cone defined by a single homogeneous quadratic, and H is an affine hyperplane. Under several easy-to-verify conditions, we derive simple, computable convex relaxations and , where is a SOCr cone. Under further conditions, we prove that these two sets capture precisely the corresponding conic/convex hulls. Our approach unifies and extends previous results, and we illustrate its applicability and generality with many examples.
Details
- Title: Subtitle
- How to convexify the intersection of a second order cone and a nonconvex quadratic
- Creators
- Samuel Burer - University of IowaFatma Kilinc-Karzan - Carnegie Mellon Univ, Tepper Sch Business, Pittsburgh, PA 15213 USA
- Resource Type
- Journal article
- Publication Details
- Mathematical programming, Vol.162(1-2), pp.393-429
- Publisher
- Springer Nature
- DOI
- 10.1007/s10107-016-1045-z
- ISSN
- 0025-5610
- eISSN
- 1436-4646
- Number of pages
- 37
- Grant note
- 1454548 / Div Of Civil, Mechanical, & Manufact Inn; National Science Foundation (NSF); NSF - Directorate for Engineering (ENG) CMMI 1454548 / NSF; National Science Foundation (NSF)
- Language
- English
- Date published
- 03/01/2017
- Academic Unit
- Business Analytics
- Record Identifier
- 9984380429402771
Metrics
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