I am looking for fast, memory-efficient computational algorithms to solve the following problem:
Minimize: $||x - x*||_2^2$, subject to constraints $A x = a, B x <= b, l <= x <= u$,
where $x*$ is given; $x, l, u, \in R^n$, $A \in R^{m x n}$, $B \in R^{p x n}$. Note that `$n$' is very large, $O(10^4 to 10^6)$, and $m$ and $p$ are much smaller. .
My problem is to project the point $x*$ onto the nearest feasible point, where feasible region is defined by the equality, inequality, and box constraints.
Any help is greatly appreciated. Thank you.