| The quadratic penalty function method is a technique for solving the standard equality constrained optimization problem. The method was invented by Courant in 1943 but fell from favor because of numerical difficulties. There are two sources of difficulty, the more obvious of which can be ascribed to a potentially massive cancellation of digits when the Hessian of a penalty function is formed. The other source of difficulty is the apparent inability of unconstrained techniques to adequately follow level sets of the constraints. In this thesis we have directed our efforts at overcoming these problems and constructing a fast and stable algorithm. Our complete algorithm is clearly stable and we prove that it is both globally and ultimately locally Q-superlinearly convergent. |
