Semi-Parametric Dimension Reduction Models Using Orthogonality Constrained Optimization R package orthoDr version 0.6.8 Utilize an orthogonality constrained optimization algorithm of Wen & Yin (2013) <DOI:10.1007/s10107-012-0584-1> to solve a variety of dimension reduction problems in the semiparametric framework, such as Ma & Zhu (2012) <DOI:10.1080/01621459.2011.646925>, Ma & Zhu (2013) <DOI:10.1214/12-AOS1072>, Sun, Zhu, Wang & Zeng (2019) <DOI:10.1093/biomet/asy064> and Zhou, Zhu & Zeng (2021) <DOI:10.1093/biomet/asaa087>. The package also implements some existing dimension reduction methods such as hMave by Xia, Zhang, & Xu (2010) <DOI:10.1198/jasa.2009.tm09372> and partial SAVE by Feng, Wen & Zhu (2013) <DOI:10.1080/01621459.2012.746065>. It also serves as a general purpose optimization solver for problems with orthogonality constraints, i.e., in Stiefel manifold. Parallel computing for approximating the gradient is enabled through 'OpenMP'. Software Imports: Rcpp (>= 1.0.9), survival, dr, pracma, plot3D, rgl, MASS LinkingTo: Rcpp, RcppArmadillo Ruoqing Zhu <teazrq@gmail.com> Comprehensive R Archive Network (CRAN) Ruilin Zhao [aut, cph], Ruoqing Zhu [aut, cre, cph] (ORCID: <https://orcid.org/0000-0002-0753-5716>), Jiyang Zhang [aut, cph], Wenzhuo Zhou [aut, cph], Peng Xu [aut, cph], James Joseph Balamuta [ctb] (ORCID: <https://orcid.org/0000-0003-2826-8458>) GPL (>= 2) 2024-03-13 application/tgz https://CRAN.R-project.org/package=orthoDr doi:10.32614/CRAN.package.orthoDr