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

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

manifold, Riemannian, Grassmann, Stiefel, Euclidean, optimization.

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.

Sean R. Martin

https://www.jstatsoft.org/article/view/v093i01

University of Maryland,
Baltimore County

February 2020

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