I want to find the projection of a vector called "a" on a closed and convex set with linear constraints. The set is in the following form:

Ax=b

Bx<=d

x>=0

I know I need to solve the following problem to get the projection:

minimize ||x-a||^2

Ax=b

Bx<=d

x>=0

However, it takes a long time when I optimize it using CPLEX since it is a large scale problem with millions of variables and I need to optimize it thousands of times for convergence. I was wondering if there is an efficient way to solve this problem using CPLEX.

Thanks for your time and help.