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 …

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 …

Variance reduction is popular in accelerating gradient descent and stochastic gradient
descent for optimization problems defined on both euclidean space and Riemannian …

Many learning tasks are modeled as optimization problems with nonlinear constraints, such
as principal component analysis and fitting a Gaussian mixture model. A popular way to …

Contemporary advances in the field of deep learning have embarked upon an exploration of
the underlying geometric properties of data, thus encouraging the investigation of …

We consider an inexact variant of the popular Riemannian trust-region algorithm for
structured big-data minimization problems. The proposed algorithm approximates the …

This paper studies large-scale optimization problems on Riemannian manifolds whose
objective function is a finite sum of negative log-probability losses. Such problems arise in …