Corpus ID: 52826032

A Riemannian approach to low-rank algebraic Riccati equations

  title={A Riemannian approach to low-rank algebraic Riccati equations},
  author={Bamdev Mishra and B. Vandereycken},
  journal={arXiv: Optimization and Control},
  • Bamdev Mishra, B. Vandereycken
  • Published 2013
  • Mathematics
  • arXiv: Optimization and Control
  • We propose a Riemannian optimization approach for computing low-rank solutions of the algebraic Riccati equation. The scheme alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is on the set of fixed-rank symmetric positive definite matrices which is endowed with a particular Riemannian metric (and geometry) that is tuned to the structure of the objective function. We specifically discuss the implementation of a Riemannian trust-region algorithm that is… CONTINUE READING
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