An efficient algorithm for solving the unconstrained nonlinear multivariable minimization problems

Abstract

This paper presents an efficient method, referred to as the Sherif-Boice Algorithm (SBA) for the solution of the unconstrained nonlinear multivariable minimization problems. The method is a sequential search routine for minimizing a function F( x ) of more than one variable, X = ( X 1, X 2,…, X r ). The procedure consists of two types of move: Exploratory and Pattern. The exploratory move resembles that of Hooke and Jeeves; however, the new method utilizes a parsimonious pattern move procedure that eliminates unnecessary exploratory moves around a failed pattern move. Numerical examples are given to show the high efficiency of the present method.