I have generated a NxN matrix (V) as a CVX optimal solution. Now I want to generate rank one 1xN matrix, v, from the NxN matrix, V, by utilizing the Gaussian randomization method. Anyone, pl help

I don’t know much about the Gaussian randomization method, but it appears to be a way of recovering an approximate solution to a problem by post-processing the optimal solution of a relaxed (omitting rank one constraint) problem. As such, it does not appear to directly involve any optimization, beyond solving the relaxed problem, which you have already done.

Before posting for help here or at https://www.mathworks.com/matlabcentral/answers/1751830-find-rank-one-1xn-matrix-from-the-nxn-matrix-by-utilizing-the-gaussian-randomization-method/?s_tid=ans_lp_feed_leaf , it would serve you well to study the mathematics (mathematical steps) of the Gaussian randomization method, rather than just blindly posting for help. If those steps don’t involve any further convex optimization problems (which I don’t think they do, unless feeding the result into a subsequent optimization problem), this forum would not be the appropriate place to seek additional help. if you have been assigned by an advisor to do this, then I suppose your advisor expects you to put in the effort to study the method you are to apply.