# orthoDr: Semiparametric Dimension Reduction via Orthogonality Constrained Optimization

Published in The R Journal, 2019

Recommended citation: Ruoqing Zhu, Jiyang Zhang, Ruilin Zhao, Peng Xu, Wenzhuo Zhou, Xin Zhang. "orthoDr: Semiparametric Dimension Reduction via Orthogonality Constrained Optimization." The R Journal. Jul 2019.

## Abstract

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 Wen and Yin (2012) 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.