Fenchel Duality and a Separation Theorem on Hadamard Manifolds

DOI10.1137/21M1400699OpenAlexW3130557384WikidataQ113779057 ScholiaQ113779057MaRDI QIDQ5080506

Maurício Silva Louzeiro, Ronny Bergmann, Roland Griesse

Publication date: 31 May 2022

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.11155

zbMATH Keywords

Riemannian manifoldconvex analysisHadamard manifoldFenchel conjugate function

Mathematics Subject Classification ID

Convex programming (90C25) Convexity of real functions of several variables, generalizations (26B25)

Related Items

Fenchel conjugate via Busemann function on Hadamard manifolds, Basic Convex Analysis in Metric Spaces with Bounded Curvature, Unnamed Item

Cites Work

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• Restoration of manifold-valued images by half-quadratic minimization
• Duality and subdifferential for convex functions on complete \(CAT(0)\) metric spaces
• Riemannian geometry for the statistical analysis of diffusion tensor data
• Functional analysis, Sobolev spaces and partial differential equations
• Conjugate duality in convex optimization
• Subgradient algorithm on Riemannian manifolds
• Smooth nonlinear optimization of \(\mathbb R^n\)
• Priors with coupled first and second order differences for manifold-valued image processing
• A first-order primal-dual algorithm for convex problems with applications to imaging
• Design of experiments in nonlinear models. Asymptotic normality, optimality criteria and small-sample properties
• Simple algorithms for optimization on Riemannian manifolds with constraints
• Fenchel duality theory and a primal-dual algorithm on Riemannian manifolds
• A Second Order Nonsmooth Variational Model for Restoring Manifold-Valued Images
• Minimum-Volume Ellipsoids
• Low-Rank Matrix Completion by Riemannian Optimization
• Convex analysis and optimization in Hadamard spaces
• Low-Rank Optimization on the Cone of Positive Semidefinite Matrices
• A Parallel Douglas–Rachford Algorithm for Minimizing ROF-like Functionals on Images with Values in Symmetric Hadamard Manifolds
• First Order Methods for Optimization on Riemannian Manifolds
• Proximal Point Algorithm On Riemannian Manifolds
• Introduction to Riemannian Manifolds
• Geodesic Convexity and Covariance Estimation
• A primal–dual hybrid gradient method for nonlinear operators with applications to MRI
• Total Variation Regularization for Manifold-Valued Data
• Operator scaling via geodesically convex optimization, invariant theory and polynomial identity testing
• Conic Geometric Optimization on the Manifold of Positive Definite Matrices
• Functions of Matrices
• Convex Analysis
• Convex analysis and monotone operator theory in Hilbert spaces
• Riemannian geometry and geometric analysis