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Quadratic Cone Cutting Surfaces for Quadratic Programs with On-Off Constraints

Hyemin Jeon(jeon5***at***wisc.edu)
Jeff Linderoth(linderoth***at***wisc.edu)
Andrew Miller(foresomenteneikona***at***gmail.com)

Abstract: We study the convex hull of a set arising as a relaxation of difficult convex mixed integer quadratic programs (MIQP). We characterize the extreme points of our set and the extreme points of its continuous relaxation. We derive four quadratic cutting surfaces that improve the strength of the continuous relaxation. Each of the cutting surfaces is second-order-cone representable. Via a shooting experiment, we provide empirical evidence as to the importance of each inequality type in improving the relaxation. Computational results that employ the new cutting surfaces to strengthen the relaxation for MIQPs arising from portfolio optimization applications are promising.


Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Linear, Cone and Semidefinite Programming (Second-Order Cone Programming )


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Entry Submitted: 01/16/2015
Entry Accepted: 01/19/2015
Entry Last Modified: 01/16/2015

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