Machine learning develops rapidly, which has made many theoretical breakthroughs and is
widely applied in various fields. Optimization, as an important part of machine learning, has …

Manifold optimization is ubiquitous in computational and applied mathematics, statistics,
engineering, machine learning, physics, chemistry, etc. One of the main challenges usually …

The well-designed structures in neural networks reflect the prior knowledge incorporated
into the models. However, though different models have various priors, we are used to …

We consider the vector embedding problem. We are given a finite set of items, with the goal
of assigning a representative vector to each one, possibly under some constraints (such as …

Projection robust Wasserstein (PRW) distance, or Wasserstein projection pursuit (WPP), is a
robust variant of the Wasserstein distance. Recent work suggests that this quantity is more …

From optimal transport to robust dimensionality reduction, many machine learning
applicationscan be cast into the min-max optimization problems over Riemannian manifolds …

Kohn–Sham density functional theory (DFT) is the most widely used electronic structure
theory. Despite significant progress in the past few decades, the numerical solution of Kohn …

In this paper, we focus on the decentralized optimization problem over the Stiefel manifold,
which is defined on a connected network of agents. The objective is an average of local …

Abstract KSSOLV (Kohn-Sham Solver) is a MATLAB toolbox for performing Kohn-Sham
density functional theory (DFT) calculations with a plane-wave basis set. KSSOLV 2.0 …

Almost all point clouds denoising methods contain various parameters, which need to be set
carefully to acquire desired results. In this paper, we introduce an evolutionary optimization …