THE APPLICATION OF A NONLINEAR PROGRAMMING ALGORITHM TO A SECOND ORDER REPRESENTATION OF THE PROBLEM

Abstract : Recently several algorithms have been presented for the solution of nonlinear programming problems. Examples of such work are the procedures of Rosen, Zoutendijk, Fiacco and McCormick, and Graves. In contrast to the amount of theoretical activity, relatively little work has been published on the computational aspects of the algorithms. This paper describes some computational experiments in the area of nonlinear programming. Specifically, working within the framework of an algorithm developed by G. Graves, the authors shall compare the convergence using only first derivatives with the convergence obtained when the algorithm is applied to an expanded natural second order form of the problem requiring second derivatives. First they provide a general description of the nonlinear algorithm with a proof of convergence. Next they give a natural second order form of the problem. Finally, the computational results for four nonlinear problems recently circulated by A. R. Colville of I.B.M. are presented. (Author)