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

Ksenia Bestuzheva (), Hassan Hijazi () and Carleton Coffrin ()
Additional contact information
Ksenia Bestuzheva: Data61-CSIRO, Australian National University, Canberra 2601, Australia; Zuse Institute Berlin, 14195 Berlin, Germany
Hassan Hijazi: Los Alamos National Laboratory, Los Alamos, New Mexico 87545
Carleton Coffrin: Los Alamos National Laboratory, Los Alamos, New Mexico 87545

INFORMS Journal on Computing, 2020, vol. 32, issue 3, 682-696

Abstract: This paper studies mixed-integer nonlinear programs featuring disjunctive constraints and trigonometric functions and presents a strengthened version of the convex quadratic relaxation of the optimal transmission switching problem. 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 bound propagation, on 23 medium-sized test cases in the PGLib benchmark library with a relaxation gap of more than 1%, we reduce the gap to less than 1% on five instances. The tightened model has promising computational results when compared with state-of-the-art formulations.

Keywords: mixed-integer nonlinear programming; perspective relaxation; on/off constraints; optimal transmission switching; trigonometric functions (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://doi.org/10.1287/ijoc.2019.0900 (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:orijoc:v:32:y:3:i:2020:p:682-696

Access Statistics for this article

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