# A Low-Rank Coordinate-Descent Algorithm for Semidefinite Programming Relaxations of Optimal Power Flow

arXiv: https://arxiv.org/abs/1506.08568 · HTML: https://mlsanity.com/paper/1506.08568/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2015.

## Built on by (most cited first, 2 of 2)

- [A Non-commutative Extension of Lee-Seung's Algorithm for Positive Semidefinite Factorizations](https://mlsanity.com/paper/2106.00293/) (2021)
- [Inference and Optimization for Engineering and Physical Systems](https://mlsanity.com/paper/2208.13880/) (2022)

## Abstract (arXiv)

The alternating-current optimal power flow (ACOPF) is one of the best known non-convex non-linear optimisation 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 SDP 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.