Grassmannoptim: An R package for Grassmann manifold optimization

Kofi Placid Adragni, R. Dennis Cook, Seongho Wu

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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 languageEnglish (US)
JournalJournal of Statistical Software
StatePublished - Jul 2012


  • Constrained optimization
  • Grassmann manifold
  • Simulated annealing


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