An efficient method for unconstrained optimization problems of nonlinear large mesh-interconnected systems

Presents an 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. The authors prove that their 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, the authors observe that their 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