The optimization of a real-valued objective function f (U), where U is a p × d, p > d, semi-orthogonal matrix such that UTU = Id, 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.
|Original language||English (US)|
|Journal||Journal of Statistical Software|
|State||Published - Jul 1 2012|
- Constrained optimization
- Grassmann manifold
- Simulated annealing