Single index model (SIM) is an important semi-parametric extension of linear models. In this ongoing work, we consider a shape constrained high dimensional SIM (hdSIM), where the link function is monotonic (but not necessarily smooth) and the coefficient parameter is high dimensional and sparse. We propose a scalable projection-based iterative approach, namely  the  “orthogonal  gradient single-index model” (OG-SIM) algorithm, which alternates between sparse-thresholded orthogonalized gradient steps and isotonic regression steps to recover the coefficient vector. We show theoretical guarantees for the estimation of both the link function and the coefficient parameter. Our theoretical work will be based on very mild assumptions on the design matrix X and error term. In particular, X can be fixed or random. If X is random, it can be asymmetric and the error distribution can depend on X. We study the performance of our algorithm via both numerical studies and also an application on a rocker protein sequence data. This is joint work with Hyebin Song, Rina Foygel Barber, and Garvesh Raskutti.