GrassmannOptim: An R Package for Grassmann Manifold Optimization

Abstract

The optimization of a real-valued objective function f(U), where U is a p X d,p > d, semi-orthogonal matrix such that U^TU=I_d, and f is invariant under right orthogonal transformation of U, is often referred to as a Grassmann manifold optimization. Manifold optimization appears in a wide variety of computational problems in the applied sciences. In this article, we present GrassmannOptim, an R package for Grassmann manifold optimization. The implementation uses gradient-based algorithms and embeds a stochastic gradient method for global search. We describe the algorithms, provide some illustrative examples on the relevance of manifold optimization and finally, show some practical usages of the package.