Abstract
This paper extends the existing penalty methods for obtaining the local solutions of a general class of nonlinear programming problems. The principal motivation is the elimination of the restrictions of the interior point method and the exterior point method. The interior point method requires the nonempty feasible region and the exterior point method lacks the order of differentiability of the penalty function at any boundary point of the feasible region.
We present a new class of penalty function and prove that it possesses the properties of the generalized penalty function. The algorithm proposed is termed SUMUP (Sequential Unconstrained Method Using Penalty). This penalty function has the features that it contains the constants corresponding to Lagrange multipliers and it is twice differentiable at the boundary of the feasible region. By choosing properly the constants (Lagrange multipliers), the SUMUP algorithm can approach the optimum from the region of feasibility or infeasibility.
The penalty function for SUMUP is shown to be the generalized form of the functions for the interior and exterior point methods.
