We consider a class of nonsmooth optimization problems over the Stiefel manifold, in which
the objective function is weakly convex in the ambient Euclidean space. Such problems are …

Contraction analysis considers the distance between two adjacent trajectories. If this
distance is contracting, then trajectories have the same long-term behavior. The main …

We develop a manifold inexact augmented Lagrangian framework to solve a family of
nonsmooth optimization problem on Riemannian submanifold embedding in Euclidean …

We propose a subgradient algorithm for the computation of contraction metrics for systems
with an exponentially stable equilibrium. We show that for sufficiently smooth systems our …

We study the convergence analysis of the incremental quasi-subgradient method for solving
the sum of geodesic quasi-convex functions on Riemannian manifolds whose sectional …

We design and implement a Python library to help the non-expert using all these powerful
tools in a way that is efficient, extensible, and simple to incorporate into the workflow of the …

Sparse principal component analysis (PCA) improves interpretability of the classic PCA by
introducing sparsity into the dimension-reduction process. Optimization models for sparse …

In the remote state estimation problem, an observer tries to reconstruct the state of a
dynamical system at a remote location, where no direct sensor measurements are available …

We give curvature-dependant convergence rates for the optimization of weakly convex
functions defined on a manifold of 1-bounded geometry via Riemannian gradient descent …

In this paper, we extend a recently established subgradient method for the computation of
Riemannian metrics that optimizes certain singular value functions associated with …