First- and Second-Order Analysis for Optimization Problems with Manifold-Valued Constraints
Optimization and Control
2024-02-23 v2
Abstract
We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the codomain of the constraint mapping are smooth manifolds. We model the feasible set as the preimage of a submanifold with corners of the codomain. The latter is a subset which corresponds to a convex cone locally in suitable charts. We study first- and second-order optimality conditions for this class of problems. We also show the invariance of the relevant quantities with respect to local representations of the problem.
Cite
@article{arxiv.2110.04882,
title = {First- and Second-Order Analysis for Optimization Problems with Manifold-Valued Constraints},
author = {Ronny Bergmann and Roland Herzog and Julián Ortiz López and Anton Schiela},
journal= {arXiv preprint arXiv:2110.04882},
year = {2024}
}