OPTIMIZATION OF NONLINEAR PROGRAMMING PROBLEMS USING PENALTY FUNCTIONS AND COMPLEX METHOD

Abstract

Here the validity of a no-derivative Complex Method for the optimization of constrained nonlinear programming (NLP) problems is discussed. This method, starting with N (N>__-n+1, where n is the dimension of the problem) feasible points, determines the optimum by a typical descent method. Though this method is capable of determining a nearly optimal feasible solution, its convergence in the general case is not guaranteed. However, this method has good convergence properties for unconstrained problems; hence transformation of the constrained NLP problem to a series of smooth unconstrained problems by the use of a penalty function and the application of the complex method to these functions is proposed for the determination of the optimum. A number of problems are solved by the complex method as well as by the use of a penalty function and the complex method, and the results are compared.