would like to address all concerns raised. please find some details regarding the proposed methods

We would like to thank all of the reviewers for their valuable time and their constructive comments. Reviewer 1: We will incorporate the proposed minor corrections in the final version of the paper. The two-stage approach, i.e., i) running gradient descent to convergence, and then ii) projection onto sparsity set, On whether support set changes during iterations, we observe that in experiments (subsection 4.1) IHT changes support, Reviewer 2: We thank the reviewer for the supportive and constructive review. Regarding the comment in lines 198-202, we apologize for any confusion. Regarding variance in experiments, we have observed high variance is not enough for the algorithm to get "lucky".