Newton's Method for Generalized Equations.

Abstract : Newton's method is a well known and often applied technique for computing a zero of a nonlinear function. By using the theory of generalized equations, a Newton method is developed to solve problems arising in both mathematical programming and mathematical economics. Two results concerning the convergence and convergence rate of Newton's method are proved for generalized equations. Examples are given to emphasize the application of this method to generalized equations representing the non-linear programming problem and the nonlinear complementarity problem. Computational results of Newton's method applied to a nonlinear complementarity problem of Kojima, and an invariant capital stock problem of Hansen and Koopmans are both presented.