Abstract
The field of nonlinear programming has witnessed a tremendous growth in the last several years. However, to some extent, nonlinear programming exists as an experimental field of research, advancing through the study of particular algorithms, investigation of the results on specific problems, and construction of better algorithms based on the experience. With improvements in computers and the growing need to more accurately represent the problems of the real world, there is a need for more reliable methods of optimizing nonlinear objective functions. A sequentially transforming conjugate algorithm has been developed. The algorithm utilizes two different coordinate systems to locate the optimal solution. One of the systems is the space of variables in which the problem is originally posed, while the other is a transformed space which is sequentially determined by information collected about the objective function via a sequence of conjugative gradient searches. The purpose of the sequentially defined coordinate system is to develop a system in which the contour surfaces of the nonlinear objective function are approximately spherical. Through the development of the spherical nature of the objective function in the sequentially defined coordinate system, two additional properties of the proposed algorithm will be derived. These two properties will mainly be concerned with creating a more advantageous unidimensional line than is possible with a straightforward approach of line search techniques. The newly developed algorithm will be incorporated into a computer model and its relative effectiveness will be determined by comparison with one of the best existing conjugative gradient algorithms, the Davidon-Fletcher-Powell Algorithm. The basis for the comparison will be a series of test functions which include differing numbers of variable and varying degrees of nonlinearity. A sensitivity analysis of several of the more important quantities involved in the algorithm is also included.
Rappold, Robert Allen (1974). A sequentially transforming conjugate gradient algorithm. Doctoral dissertation, Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -172608.