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

Mathematical optimization is an important branch of applied mathematics. Different classes
of optimization problems are categorized based on their problem structures. While there are …

In recent years, stochastic variance reduction algorithms have attracted considerable
attention for minimizing the average of a large but finite number of loss functions. This paper …

The minimax optimization over Riemannian manifolds (possibly nonconvex constraints) has
been actively applied to solve many problems, such as robust dimensionality reduction and …

Abstract SPIDER (Stochastic Path Integrated Differential EstimatoR) is an efficient gradient
estimation technique developed for non-convex stochastic optimization. Although having …

Stochastic and finite-sum optimization problems are central to machine learning. Numerous
specializations of these problems involve nonlinear constraints where the parameters of …

Adaptive stochastic gradient algorithms in the Euclidean space have attracted much
attention lately. Such explorations on Riemannian manifolds, on the other hand, are …

In this paper, we study min-max optimization problems on Riemannian manifolds. We
introduce a Riemannian Hamiltonian function, minimization of which serves as a proxy for …

In the paper, we study a class of useful minimax problems on Riemanian manifolds and
propose a class of effective Riemanian gradient-based methods to solve these minimax …

In this paper, we introduce McTorch, a manifold optimization library for deep learning that
extends PyTorch. It aims to lower the barrier for users wishing to use manifold constraints in …