Newton-type methods for nonlinearly constrained programming problems-algorithms and theory

For optimization problems including inequality constraints the well-known locally and superlinealy convergent methods of Levitin/Polyak, of Robinson and of Wilson (Recursive Quadratic Programming) lead to inequality constrained nonlinear subproblems. In the present paper optimization methods are introduced which are also locally and superlinearly convergent, but in contrast to the methods mentioned above the occurring subproblems are systems of linear equations. This results from the fact that the methods proposed are based on Newton's method for solving nonlinear equations.