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Title: Convex quadratic relaxations for mixed-integer nonlinear programs in power systems

Here, this paper presents a set of new convex quadratic relaxations for nonlinear and mixed-integer nonlinear programs arising in power systems. The considered models are motivated by hybrid discrete/continuous applications where existing approximations do not provide optimality guarantees. The new relaxations offer computational efficiency along with minimal optimality gaps, providing an interesting alternative to state-of-the-art semidefinite programming relaxations. Finally, three case studies in optimal power flow, optimal transmission switching and capacitor placement demonstrate the benefits of the new relaxations.
Authors:
ORCiD logo [1] ; ORCiD logo [2] ;  [3]
  1. The Australian National University, Canberra (Australia)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  3. Univ. of Michigan, Ann Arbor, MI (United States)
Publication Date:
Report Number(s):
LA-UR-18-21065
Journal ID: ISSN 1867-2949
Grant/Contract Number:
AC52-06NA25396
Type:
Accepted Manuscript
Journal Name:
Mathematical Programming Computation
Additional Journal Information:
Journal Volume: 9; Journal Issue: 3; Journal ID: ISSN 1867-2949
Publisher:
Springer
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE Laboratory Directed Research and Development (LDRD) Program
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 42 ENGINEERING; Mixed-integer nonlinear programming; Global optimization; Convex relaxation; Optimal power flow; Optimal transmission switching; Capacitor placement
OSTI Identifier:
1469547

Hijazi, Hassan Lionel, Coffrin, Carleton James, and Hentenryck, Pascal Van. Convex quadratic relaxations for mixed-integer nonlinear programs in power systems. United States: N. p., Web. doi:10.1007/s12532-016-0112-z.
Hijazi, Hassan Lionel, Coffrin, Carleton James, & Hentenryck, Pascal Van. Convex quadratic relaxations for mixed-integer nonlinear programs in power systems. United States. doi:10.1007/s12532-016-0112-z.
Hijazi, Hassan Lionel, Coffrin, Carleton James, and Hentenryck, Pascal Van. 2016. "Convex quadratic relaxations for mixed-integer nonlinear programs in power systems". United States. doi:10.1007/s12532-016-0112-z. https://www.osti.gov/servlets/purl/1469547.
@article{osti_1469547,
title = {Convex quadratic relaxations for mixed-integer nonlinear programs in power systems},
author = {Hijazi, Hassan Lionel and Coffrin, Carleton James and Hentenryck, Pascal Van},
abstractNote = {Here, this paper presents a set of new convex quadratic relaxations for nonlinear and mixed-integer nonlinear programs arising in power systems. The considered models are motivated by hybrid discrete/continuous applications where existing approximations do not provide optimality guarantees. The new relaxations offer computational efficiency along with minimal optimality gaps, providing an interesting alternative to state-of-the-art semidefinite programming relaxations. Finally, three case studies in optimal power flow, optimal transmission switching and capacitor placement demonstrate the benefits of the new relaxations.},
doi = {10.1007/s12532-016-0112-z},
journal = {Mathematical Programming Computation},
number = 3,
volume = 9,
place = {United States},
year = {2016},
month = {10}
}