TY - JOUR
AU - Adragni, Kofi Placid
AU - Cook, R. Dennis
AU - Wu, Seongho
PY - 2012/07/20
Y2 - 2023/12/05
TI - GrassmannOptim: An R Package for Grassmann Manifold Optimization
JF - Journal of Statistical Software
JA - J. Stat. Soft.
VL - 50
IS - 5
SE - Articles
DO - 10.18637/jss.v050.i05
UR - https://www.jstatsoft.org/index.php/jss/article/view/v050i05
SP - 1 - 18
AB - The optimization of a real-valued objective function <i>f</i>(<b>U</b>), where <b>U</b> is a <i>p</i> X <i>d,p</i> > <i>d</i>, semi-orthogonal matrix such that <b>U</b><sup>T</sup><b>U</b>=<b>I</b><sub>d</sub>, and <i>f</i> is invariant under right orthogonal transformation of <b>U</b>, 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 <b>GrassmannOptim</b>, 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.
ER -