Optimization Methods for Box-Constrained Nonlinear Programming Problems Based on Linear Transformation and Lagrange Interpolating Polynomials

In this paper, an optimality condition for nonlinear programming problems with box constraints is given by using linear transformation and Lagrange interpolating polynomials. Based on this condition, two new local optimization methods are developed. The solution points obtained by the new local optimization methods can improve the Karush–Kuhn–Tucker (KKT) points in general. Two global optimization methods then are proposed by combining the two new local optimization methods with a filled function method. Some numerical examples are reported to show the effectiveness of the proposed methods. © 2017, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag Berlin Heidelberg.