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.