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Geodesic convexity generalizes the notion of (vector space) convexity to nonlinear metric spaces.
Manifolds of negative curvature
Richard L Bishop and Barrett O’Neill · 1969
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A.D. Alexandrov spaces with curvature bounded below
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Convex functions and optimization methods on Riemannian manifolds , volume 297
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The geometry of algorithms with orthogonality constraints
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Metric spaces of non-positive curvature , volume 319
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Geometry of the space of phylogenetic trees
Louis J Billera, Susan P Holmes, and Karen Vogtmann · 2001
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A course in metric geometry , volume 33
Dmitri Burago, Yuri Burago, and Sergei Ivanov · 2001
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A riemannian interpolation inequality à la borell, brascamp and lieb
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A tutorial on geometric programming
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Riemannian geometry for the statistical analysis of diffusion tensor data
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Fast kernel-based independent component analysis
Hao Shen, Stefanie Jegelka, and Arthur Gretton · 2009
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Computing the karcher mean of symmetric positive definite matrices
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Stochastic gradient descent on riemannian manifolds
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Low-rank optimization with trace norm penalty
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Low-rank matrix completion by riemannian optimization
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Multivariate generalized Gaussian distribution: Convexity and graphical models
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On accelerated proximal gradient methods for convex-concave optimization. 2008
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Mariya Ishteva, P-A Absil, Sabine Van Huffel, and Lieven De Lathauwer · 2011
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Sparse coding and dictionary learning for symmetric positive definite matrices: A kernel approach
Mehrtash T Harandi, Conrad Sanderson, Richard Hartley, and Brian C Lovell · 2012
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Maximization of matrix trace function of product stiefel manifolds
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Conic Geometric Optimization on the Manifold of Positive Definite Matrices
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Complete dictionary recovery over the sphere ii: Recovery by riemannian trust-region method
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