Conic Geometric Optimization on the Manifold of Positive Definite Matrices

  title={Conic Geometric Optimization on the Manifold of Positive Definite Matrices},
  author={S. Sra and R. Hosseini},
  journal={SIAM J. Optim.},
  • S. Sra, R. Hosseini
  • Published 2015
  • Mathematics, Computer Science
  • SIAM J. Optim.
  • We develop geometric optimization on the manifold of Hermitian positive definite (HPD) matrices. In particular, we consider optimizing two types of cost functions: (i) geodesically convex (g-convex) and (ii) log-nonexpansive (LN). G-convex functions are nonconvex in the usual Euclidean sense but convex along the manifold and thus allow global optimization. LN functions may fail to be even g-convex but still remain globally optimizable due to their special structure. We develop theoretical tools… CONTINUE READING
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