On solving equations arising from optimization problems by some generalized newton method

摘要

In this paper we consider equations arising from an optimization problem by the Lagrangian method and show a new algorithm for solving the equations by a generalized Newton method. In a finite number of iterations we can find matrices which are closed to the inverse of the Jacobian matrix by the generalized Newton method.Moreover we get the superlinear convergence to the optimal solution of the optimization problem from our theorem.