Low-Rank Optimization on the Cone of Positive Semidefinite Matrices

  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},
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
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Constructing retractions on matrix manifolds, in preparation

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Geometric Algorithms for Component Analysis with a View to Gene Expression Data Analysis

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