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Mathematical Problems in Engineering
Volume 2014, Article ID 563860, 5 pages
Research Article

Global Minimization of Nonsmooth Constrained Global Optimization with Filled Function

1Department of Mathematics, Shanghai Second Polytechnic University, Shanghai 201209, China
2Department of Mathematics, Henan University of Science and Technology, Luoyang 471003, China
3Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China

Received 17 May 2014; Accepted 29 August 2014; Published 25 September 2014

Academic Editor: Sergio Preidikman

Copyright © 2014 Wei-xiang Wang et al. 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.


A novel filled function is constructed to locate a global optimizer or an approximate global optimizer of smooth or nonsmooth constrained global minimization problems. The constructed filled function contains only one parameter which can be easily adjusted during the minimization. The theoretical properties of the filled function are discussed and a corresponding solution algorithm is proposed. The solution algorithm comprises two phases: local minimization and filling. The first phase minimizes the original problem and obtains one of its local optimizers, while the second phase minimizes the constructed filled function and identifies a better initial point for the first phase. Some preliminary numerical results are also reported.