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Journal of Applied Mathematics
Volume 2011, Article ID 478608, 17 pages
http://dx.doi.org/10.1155/2011/478608
Research Article

Complete Solutions to General Box-Constrained Global Optimization Problems

Department of Mathematics, Henan University of Science and Technology, Luoyang 471003, China

Received 17 March 2011; Accepted 16 May 2011

Academic Editor: Juan Manuel Peña

Copyright © 2011 Dan Wu and Youlin Shang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper presents a global optimization method for solving general nonlinear programming problems subjected to box constraints. Regardless of convexity or nonconvexity, by introducing a differential flow on the dual feasible space, a set of complete solutions to the original problem is obtained, and criteria for global optimality and existence of solutions are given. Our theorems improve and generalize recent known results in the canonical duality theory. Applications to a class of constrained optimal control problems are discussed. Particularly, an analytical form of the optimal control is expressed. Some examples are included to illustrate this new approach.