We present a new efficient method for solving unconstrained optimization problems for nonlinear large mesh-interconnected systems. This method combines an approximate scaled gradient method with a block Gauss-Seidel with line search method which is used to obtain an approximate solution of the unconstrained quadratic programming subproblem. We prove that our method is globally convergent and demonstrate by several numerical examples its superior efficiency compared to a sparse matrix technique based method. In an example of a system of more than 200 variables, we observe that our method is 3.45 times faster than the sparse matrix technique based Newton-like method and about 50 times faster than the Newton-like method without the sparse matrix technique.