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2014 A New Global Optimization Algorithm for Solving a Class of Nonconvex Programming Problems
Xue-Gang Zhou, Bing-Yuan Cao
J. Appl. Math. 2014: 1-10 (2014). DOI: 10.1155/2014/697321

Abstract

A new two-part parametric linearization technique is proposed globally to a class of nonconvex programming problems (NPP). Firstly, a two-part parametric linearization method is adopted to construct the underestimator of objective and constraint functions, by utilizing a transformation and a parametric linear upper bounding function (LUBF) and a linear lower bounding function (LLBF) of a natural logarithm function and an exponential function with e as the base, respectively. Then, a sequence of relaxation lower linear programming problems, which are embedded in a branch-and-bound algorithm, are derived in an initial nonconvex programming problem. The proposed algorithm is converged to global optimal solution by means of a subsequent solution to a series of linear programming problems. Finally, some examples are given to illustrate the feasibility of the presented algorithm.

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Xue-Gang Zhou. Bing-Yuan Cao. "A New Global Optimization Algorithm for Solving a Class of Nonconvex Programming Problems." J. Appl. Math. 2014 1 - 10, 2014. https://doi.org/10.1155/2014/697321

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07010716
MathSciNet: MR3176826
Digital Object Identifier: 10.1155/2014/697321

Rights: Copyright © 2014 Hindawi

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