I need to solve the following SOCP in Matlab:
argmin_x ||R*x||_2 s.t. s^H * x = 1 and ||x||_2 < d,
where x is an Nx1 vector and R is an MxN matrix.
CVX can solve this type of problem. However, CVX requires me to give R and does not allow me to instead give a function handle that will return R*x. This is a problem for me since once R becomes large, computing R*x directly takes too long. There exists an efficient algorithm for computing R*x that I would like to take advantage of, so I am hoping that there is another SOCP solver that I could use.