Function Optimization Using Quadratically Convergent Algorithms With One Dimensional Search Schemes

In this paper, a unified method to construct a quadratically convergent algorithm with one dimensional search schemes is described. With this method, a generalized algorithm is derived. As it's particular cases, three quadratically convergent algorithms are performed. They are the rank-one algorithm (Algorithm I), projection algorithm (Algorithm II) and the Fletcher-Reeves algorithm (Algorithm III). As one-dimensional search schemes, the golden-ratio method and dichotomous search are used. Additionally, their computer programming is developed for actual application. The use of this program is provided with the explanation of how to use it, the illustrative examples that are both quadratic and nonquadratic problems and their output. Finally, from the computer output, each algorithm was analyzed from the standpoint of efficiency for performance.