Conjugate gradient methods are important first-order optimization algorithms both in
Euclidean spaces and on Riemannian manifolds. However, while various types of conjugate …

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

The phenotypes of complex biological systems are fundamentally driven by various multi-
scale mechanisms. Multi-modal data, such as single-cell multi-omics data, enable a deeper …

This paper is devoted to the numerical solution of constrained energy minimization problems
arising in computational physics and chemistry such as the Gross–Pitaevskii and Kohn …

This paper addresses the numerical solution of nonlinear eigenvector problems such as the
Gross–Pitaevskii and Kohn–Sham equation arising in computational physics and chemistry …

Sparse models retain valuable properties to prevent over-fitting issues and improve models'
interpretability, which are important for tasks such as anomaly detection in large-scale …

Abstract Recently, the approximate Karush–Kuhn–Tucker (AKKT) conditions, also called the
sequential optimality conditions, have been proposed for nonlinear optimization in …

Variational Bayes (VB) has become a widely-used tool for Bayesian inference in statistics
and machine learning. Nonetheless, the development of the existing VB algorithms is so far …

Extracting meaningful information from noisy high-dimensional data is attracting increasing
attention as richer and higher resolution data is being collected and used for transportation …

Since optimization on Riemannian manifolds relies on the chosen metric, it is appealing to
know that how the performance of a Riemannian optimization method varies with different …