Burer-Monteiro ADMM for Large-scale Diagonally Constrained SDPs

We propose a bilinear decomposition for the Burer-Monteiro method for semidefinite programming and combine it with the Alternating Direction Method of Multipli-ers. Bilinear decomposition reduces the degree of the augmented Lagrangian from four to two, which makes each of the sub-problems a quadrati...

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Vydáno v:2022 European Control Conference (ECC) s. 66 - 71
Hlavní autoři: Chen, Yuwen, Goulart, Paul
Médium: Konferenční příspěvek
Jazyk:angličtina
Vydáno: EUCA 12.07.2022
Témata:
Computational efficiency
Convex functions
Europe
Quadratic programming
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Shrnutí:We propose a bilinear decomposition for the Burer-Monteiro method for semidefinite programming and combine it with the Alternating Direction Method of Multipli-ers. Bilinear decomposition reduces the degree of the augmented Lagrangian from four to two, which makes each of the sub-problems a quadratic programming and hence computationally efficient. Our approach is able to solve a class of large-scale SDPs with diagonal constraints. We prove that our ADMM algorithm converges globally to the set of first-order stationary points, and show empirically that the algorithm returns a globally optimal solution for diagonally constrained SDPs.
DOI:10.23919/ECC55457.2022.9838160