Perturbed variations of penalty function methods-Example: Projective SUMT

Penalty function techniques are well known perturbation methods for solving mathematical programming problems. New classes of penalty functions are defined by introducing simple perturbations of classical penalty functions or, equivalently, perturbations of the given problem. Motivation is a recently developed method called ‘Projective SUMT’, proposed by McCormick, based on solving the differential equation associated with a barrier function minimizing trajectory. It is shown that this trajectory-following algorithm is a simple variation of classical SUMT (Sequential Unconstrained Minimization Technique). This leads to numerous additional interpretations, simplified convergence results, duality relationships and extensions. Like SUMT, Projective SUMT is closely related to the approach of Karmarkar.