A Weighted Flexible Tolerance Algorithm for Constrained Minimization

Abstract

A direct search algorithm based upon the flexible tolerance method developed by Paviani and Himmelblau [1] for minimization of a functional subject to nonlinear equality and inequality constraints is proposed and evaluated. The modification incorporates a weighting on the direction of search in which the flexible polyhedron formed orients itself toward the gradient of the objective function (and clings to all active constraints). This is accomplished by weighting the centroid, in the sense of minimization, of the polyhedron with respect to the objective function. A number of problems have been solved satisfactorily by this algorithm, generally with more rapid convergence.