A low-rank coordinate-descent algorithm for semidefinite programming relaxations of optimal power flow

The alternating-current optimal power flow (ACOPF) is one of the best known non-convex nonlinear optimization problems. We present a novel re-formulation of ACOPF, which is based on lifting the rectangular power-voltage rank-constrained formulation, and makes it possible to derive alternative semide...

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Bibliographic Details
Published in:Optimization methods & software 2017-07, Vol.32 (4), p.849-871
Main Authors: Mareček, Jakub, Takáč, Martin
Format: Article
Language:English
Subjects:
Algorithms
Constraints
Descent
Electric potential
Exact solutions
Hoisting
Mathematical analysis
Mathematical programming
Nonlinearity
Optimization
Polynomials
Power flow
power system analysis
Roots
Semidefinite programming
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Summary:The alternating-current optimal power flow (ACOPF) is one of the best known non-convex nonlinear optimization problems. We present a novel re-formulation of ACOPF, which is based on lifting the rectangular power-voltage rank-constrained formulation, and makes it possible to derive alternative semidefinite programming relaxations. For those, we develop a first-order method based on the parallel coordinate descent with a novel closed-form step based on roots of cubic polynomials.
ISSN:1055-6788
1029-4937
DOI:10.1080/10556788.2017.1288729