  orthoDr is a package in R that solves dimension reduction problems using
orthogonality constrained optimization approach. The package serves as a
unified framework for many regression and survival analysis dimension reduction
models that utilize semiparametric estimating equations. The main computational
machinery of orthoDr is a first-order algorithm developed by
\cite{wen2013feasible} for optimization within the Stiefel manifold. We
implement the algorithm through Rcpp and OpenMP for fast computation. In
addition, we developed a general-purpose solver for such constrained problems
with user-specified objective functions, which works as a drop-in version of
optim(). The package also serves as a platform for future methodology
developments along this line of work.
