Conic Geometric Optimization on the Manifold of Positive Definite Matrices

@article{Sra2015ConicGO,
  title={Conic Geometric Optimization on the Manifold of Positive Definite Matrices},
  author={S. Sra and R. Hosseini},
  journal={SIAM J. Optim.},
  year={2015},
  volume={25},
  pages={713-739}
}
  • 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
    First-order Methods for Geodesically Convex Optimization
    • 108
    • PDF
    Geometric Optimization in Machine Learning
    • 14
    • PDF
    Matrix Manifold Optimization for Gaussian Mixtures
    • 40
    • PDF
    Riemannian Adaptive Optimization Methods
    • 52
    • PDF
    Accelerated First-order Methods for Geodesically Convex Optimization on Riemannian Manifolds
    • 33
    • PDF

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 70 REFERENCES
    Positive definite matrices and the S-divergence
    • 81
    • PDF
    Manopt, a matlab toolbox for optimization on manifolds
    • 563
    • PDF
    Geodesic Convexity and Covariance Estimation
    • 96
    • Highly Influential
    • PDF
    Riemannian metrics on positive definite matrices related to means
    • 76
    • PDF
    Metric Spaces of Non-Positive Curvature
    • 2,314
    The Concave-Convex Procedure
    • 945
    • PDF
    Interior-point polynomial algorithms in convex programming
    • 3,051
    • PDF
    Riemannian Dictionary Learning and Sparse Coding for Positive Definite Matrices
    • 62
    • PDF