Low-Rank Optimization on the Cone of Positive Semidefinite Matrices

@article{Journe2010LowRankOO,
title={Low-Rank Optimization on the Cone of Positive Semidefinite Matrices},
author={Michel Journ{\'e}e and Francis R. Bach and Pierre-Antoine Absil and Rodolphe Sepulchre},
journal={SIAM Journal on Optimization},
year={2010},
volume={20},
pages={2327-2351}
}

We propose an algorithm for solving optimization problems defined on a subset of the cone of symmetric positive semidefinite matrices. This algorithm relies on the factorization X = Y Y T , where the number of columns of Y fixes an upper bound on the rank of the positive semidefinite matrix X. It is thus very effective for solving problems that have a low-rank solution. The factorization X = Y Y T leads to a reformulation of the original problem as an optimization on a particular quotient… CONTINUE READING