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Mathematical Problems in Engineering
Volume 2013, Article ID 101376, 8 pages
http://dx.doi.org/10.1155/2013/101376
Review Article

A Review of Piecewise Linearization Methods

1Department of Information Technology and Management, Shih Chien University, No. 70 Dazhi Street, Taipei 10462, Taiwan
2Program in Industrial and Systems Engineering, University of Minnesota, 111 Church Street SE, Minneapolis, MN 55455, USA
3School of Information Management and Engineering, Shanghai University of Finance and Economics, Shanghai 200433, China
4School of Management, Tokyo University of Science, 500 Shimokiyoku, Kuki, Saitama 346-8512, Japan
5Department of Business Management, National Taipei University of Technology, Section 3, No. 1 Chung-Hsiao E. Road, Taipei 10608, Taiwan

Received 3 July 2013; Accepted 9 September 2013

Academic Editor: Yi-Chung Hu

Copyright © 2013 Ming-Hua Lin 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.

Abstract

Various optimization problems in engineering and management are formulated as nonlinear programming problems. Because of the nonconvexity nature of this kind of problems, no efficient approach is available to derive the global optimum of the problems. How to locate a global optimal solution of a nonlinear programming problem is an important issue in optimization theory. In the last few decades, piecewise linearization methods have been widely applied to convert a nonlinear programming problem into a linear programming problem or a mixed-integer convex programming problem for obtaining an approximated global optimal solution. In the transformation process, extra binary variables, continuous variables, and constraints are introduced to reformulate the original problem. These extra variables and constraints mainly determine the solution efficiency of the converted problem. This study therefore provides a review of piecewise linearization methods and analyzes the computational efficiency of various piecewise linearization methods.