A New Method of Constrained Optimization and a Comparison With Other Methods

Abstract

A new method for finding the maximum of a general non-linear functionof several variables within a constrained region is described, andshown to be efficient compared with existing methods when the requiredoptimum lies on one or more constraints. The efficacy of using effectiveconstraints to eliminate variables is demonstrated, and a programto achieve this easily and automatically is described. Finally, theperformance of the new method (the “Complex” method) with unconstrainedproblems, is compared with those of the Simplex method, from whichit was evolved, and Rosenbrock's method.