Given a vector y R^n, we wish to compute the optimal solution x to the optimization problem

minimize || 2 y11 subject to r1 >||(x2,..., IN) || minimize || 2 y11 subject to r1 >||(x2,..., IN) || minimize || 2 y11 subject to r1 >||(x2,..., IN) || minimize || 2 y11 subject to r1 >||(x2,..., IN) ||