A class of modified Secant methods for unconstrained optimization

摘要

A class of modified Secant methods for solving univariate and unconstrained optimization problems is presented. The class takes the classical Secant method and a new variant of the Secant method proposed in Kahya and Chen [E. Kahya, J.H. Chen, A modified Secant method for unconstrained optimization, Appl. Math. Comput. 186 (2007) 1000–1004] as its special cases. This class also includes Wang’s method with quadratical convergence proposed in Wang [X.H. Wang, Convergence iteration method of order two for finding zeros of the derivative, Math. Numer. Sinica 3 (1979) 209–220 (in Chinese)]. A unified convergence analysis as well as numerical examples show that Wang’s method is the best one among all members of the class.