
Sampling and Optimization on Convex Sets in Riemannian Manifolds of NonNegative Curvature
The Euclidean space notion of convex sets (and functions) generalizes to...
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Constant index expectation curvature for graphs or Riemannian manifolds
An integral geometric curvature is defined as the index expectation K(x)...
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CurvatureDependant Global Convergence Rates for Optimization on Manifolds of Bounded Geometry
We give curvaturedependant convergence rates for the optimization of we...
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Optimal Design of Experiments on Riemannian Manifolds
Traditional optimal design of experiment theory is developed on Euclidea...
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Spectral Residual Method for Nonlinear Equations on Riemannian Manifolds
In this paper, the spectral algorithm for nonlinear equations (SANE) is ...
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An efficient ExactPGA algorithm for constant curvature manifolds
Manifoldvalued datasets are widely encountered in many computer vision ...
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A Riemannian Corollary of Helly's Theorem
We introduce a notion of halfspace for Hadamard manifolds that is natura...
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Fenchel Duality for Convex Optimization and a Primal Dual Algorithm on Riemannian Manifolds
This paper introduces a new duality theory that generalizes the classical Fenchel conjugation to functions defined on Riemannian manifolds. This notion of conjugation even yields a more general Fenchel conjugate for the case where the manifold is a vector space. We investigate its properties, e.g., the FenchelYoung inequality and the characterization of the convex subdifferential using the analogue of the FenchelMoreau Theorem. These properties of the Fenchel conjugate are employed to derive a Riemannian primaldual optimization algorithm, and to prove its convergence for the case of Hadamard manifolds under appropriate assumptions. Numerical results illustrate the performance of the algorithm, which competes with the recently derived DouglasRachford algorithm on manifolds of nonpositive curvature. Furthermore we show that our novel algorithm numerically converges on manifolds of positive curvature.
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