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Convex Relaxations for Quadratic On/Off Constraints and Applications to Optimal Transmission Switching

Ksenia Bestuzheva(ksenija.bestuzheva***at***data61.csiro.au)
Hassan Hijazi(hassan.hijazi***at***anu.edu.au)
Carleton Coffrin(cjc***at***lanl.gov)

Abstract: This paper studies mixed-integer nonlinear programs featuring disjunctive constraints and trigonometric functions. We first characterize the convex hull of univariate quadratic on/off constraints in the space of original variables using perspective functions. We then introduce new tight quadratic relaxations for trigonometric functions featuring variables with asymmetrical bounds. These results are used to further tighten recent convex relaxations introduced for the Optimal Transmission Switching problem in Power Systems. Using the proposed improvements, along with aggressive bound propagation, we close 10 out of the 28 medium-size open test cases in the NESTA benchmark library. The tightened model has better computational results when compared to state-of-the-art formulations.

Keywords: Mixed-Integer Nonlinear Programming, Perspective Relaxation, On/Off constraints, Optimal Transmission Switching, Trigonometric Functions

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

Category 2: Applications -- Science and Engineering

Category 3: Convex and Nonsmooth Optimization (Convex Optimization )


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Entry Submitted: 07/29/2016
Entry Accepted: 07/29/2016
Entry Last Modified: 07/29/2016

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