ManifoldOptim: An R Interface to the ROPTLIB Library for Riemannian Manifold Optimization

TL;DR

ManifoldOptim is an R package that provides an interface to the ROPTLIB library, enabling efficient optimization over Riemannian manifolds for statistical and scientific applications.

Contribution

It introduces an R wrapper for ROPTLIB, facilitating R-based manifold optimization with practical examples in dimension reduction and regression.

Findings

Enables easy construction and solving of manifold optimization problems in R.

Supports integration with Rcpp for computationally intensive tasks.

Demonstrates practical applications in statistical dimension reduction and envelope methods.

Abstract

Manifold optimization appears in a wide variety of computational problems in the applied sciences. In recent statistical methodologies such as sufficient dimension reduction and regression envelopes, estimation relies on the optimization of likelihood functions over spaces of matrices such as the Stiefel or Grassmann manifolds. Recently, Huang, Absil, Gallivan, and Hand (2016) have introduced the library ROPTLIB, which provides a framework and state of the art algorithms to optimize real-valued objective functions over commonly used matrix-valued Riemannian manifolds. This article presents ManifoldOptim, an R package that wraps the C++ library ROPTLIB. ManifoldOptim enables users to access functionality in ROPTLIB through R so that optimization problems can easily be constructed, solved, and integrated into larger R codes. Computationally intensive problems can be programmed with Rcpp and RcppArmadillo, and otherwise accessed through R. We illustrate the practical use of ManifoldOptim through several motivating examples involving dimension reduction and envelope methods in regression.