Optimization on Riemannian manifolds-the result of smooth geometry and optimization
merging into one elegant modern framework-spans many areas of science and engineering …

Conjugate gradient methods are important first-order optimization algorithms both in
Euclidean spaces and on Riemannian manifolds. However, while various types of conjugate …

Manopt. jl provides a set of optimization algorithms for optimization problems given on a
Riemannian manifold M. Based on a generic optimization framework, together with the …

We describe the first gradient methods on Riemannian manifolds to achieve accelerated
rates in the non-convex case. Under Lipschitz assumptions on the Riemannian gradient and …

Interior-point methods offer a highly versatile framework for convex optimization that is
effective in theory and practice. A key notion in their theory is that of a self-concordant …

In this paper we introduce a Fenchel-type conjugate, given as the supremum of convex
functions, via Busemann functions. It is known that Busemann functions are smooth convex …

Motivated by the trade-off between noise robustness and data consistency for joint three-
imensional (3D) map reconstruction and rotation estimation in single particle cryogenic …

In this paper, we address the bounded/unbounded determination of geodesically convex
optimization on Hadamard spaces. In Euclidean convex optimization, the recession function …

When generalizing schemes for real-valued data approximation or decomposition to data
living in Riemannian manifolds, tangent space-based schemes are very attractive for the …

In this paper, we introduce a definition of Fenchel conjugate and Fenchel biconjugate on
Hadamard manifolds based on the tangent bundle. Our definition overcomes the …