Journal of Applied Mathematics

A New Global Optimization Algorithm for Solving a Class of Nonconvex Programming Problems

Xue-Gang Zhou and Bing-Yuan Cao

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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.

Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 697321, 10 pages.

Dates
First available in Project Euclid: 2 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1425305547

Digital Object Identifier
doi:10.1155/2014/697321

Mathematical Reviews number (MathSciNet)
MR3176826

Zentralblatt MATH identifier
07010716

Citation

Zhou, Xue-Gang; Cao, Bing-Yuan. A New Global Optimization Algorithm for Solving a Class of Nonconvex Programming Problems. J. Appl. Math. 2014 (2014), Article ID 697321, 10 pages. doi:10.1155/2014/697321. https://projecteuclid.org/euclid.jam/1425305547


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