First- and Second-Order Analysis for Optimization Problems with Manifold-Valued Constraints
arXiv:2110.04882 · doi:10.1007/s10208-020-09486-5
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.
References in corpus (13)
- Manopt, a Matlab toolbox for optimization on manifolds
- A combined first and second order variational approach for image reconstruction
- A primal-dual hybrid gradient method for non-linear operators with applications to MRI
- A Second Order Non-Smooth Variational Model for Restoring Manifold-Valued Images
- Restoration of Manifold-Valued Images by Half-Quadratic Minimization
- Collaborative Total Variation: A General Framework for Vectorial TV Models
- Total variation regularization for manifold-valued data
- Second Order Differences of Cyclic Data and Applications in Variational Denoising
- A Parallel Douglas Rachford Algorithm for Minimizing ROF-like Functionals on Images with Values in Symmetric Hadamard Manifolds
- Total Generalized Variation for Manifold-valued Data
- Priors with Coupled First and Second Order Differences for Manifold-Valued Image Processing
- A variational model for data fitting on manifolds by minimizing the acceleration of a Bézier curve
- A Graph Framework for Manifold-valued Data