Optimization on Weak Riemannian Manifolds
Optimization and Control
2026-04-21 v2 Differential Geometry
Abstract
Riemannian structures on infinite-dimensional manifolds arise naturally in shape analysis and shape optimization. These applications lead to optimization problems on manifolds which are not modeled on Banach spaces. The present article develops the basic framework for optimization via gradient descent on weak Riemannian manifolds leading to the notion of a Hesse manifold. Further, foundational properties for optimization are established for several classes of weak Riemannian manifolds connected to shape analysis and shape optimization.
Cite
@article{arxiv.2603.25396,
title = {Optimization on Weak Riemannian Manifolds},
author = {Valentina Zalbertus and Max Pfeffer and Alexander Schmeding},
journal= {arXiv preprint arXiv:2603.25396},
year = {2026}
}
Comments
28 pages, 2 figures, uses TikZ, v2: corrected typos and inaccuracies, main results remain unchanged