摘要：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 T U = 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.
