Four Search Method Obtaining the Conjugating Direction Along the Negative Gradient Directions

Abstract

To find a better conjugate direction, the optimization effect of six search (six-seeking) and three search method are analyzed. Because of the arbitrariness of the initial point, the first process of optimizing along the negative gradient direction is abandoned. The four search method is put forward. Each best or optimal point is the initial point of the next optimization. After three time of consecutive searches along the negative gradient directions, take the conjugate direction obtained from the second and the third optimization as the fourth search direction. That is, there are four search directions in each loop. The steps, valid mathematical proof, and program flow chart are given. A quadratic function with three variables and Rosenbrock function with two variables are used as the objective functions to verify the methods. Two examples prove the validity of the 4 search method to complex objective function. Therefore, the four search method is a better conjugate direction method.