A New Global Optimization Algorithm for Solving a Class of Nonconvex Programming Problems
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 paramet...
Main Authors: | , |
---|---|
Format: | Article |
Language: | English |
Published: |
Hindawi Limited
2014-01-01
|
Series: | Journal of Applied Mathematics |
Online Access: | http://dx.doi.org/10.1155/2014/697321 |
id |
doaj-21bcf57bc38e4c5182df3f89bbe3f574 |
---|---|
record_format |
Article |
spelling |
doaj-21bcf57bc38e4c5182df3f89bbe3f5742020-11-24T21:43:43ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/697321697321A New Global Optimization Algorithm for Solving a Class of Nonconvex Programming ProblemsXue-Gang Zhou0Bing-Yuan Cao1School of Mathematics and Information Science, Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong, Higher Education Institutes, Guangzhou University, Guangzhou, Guangdong 510006, ChinaSchool of Mathematics and Information Science, Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong, Higher Education Institutes, Guangzhou University, Guangzhou, Guangdong 510006, ChinaA 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.http://dx.doi.org/10.1155/2014/697321 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Xue-Gang Zhou Bing-Yuan Cao |
spellingShingle |
Xue-Gang Zhou Bing-Yuan Cao A New Global Optimization Algorithm for Solving a Class of Nonconvex Programming Problems Journal of Applied Mathematics |
author_facet |
Xue-Gang Zhou Bing-Yuan Cao |
author_sort |
Xue-Gang Zhou |
title |
A New Global Optimization Algorithm for Solving a Class of Nonconvex Programming Problems |
title_short |
A New Global Optimization Algorithm for Solving a Class of Nonconvex Programming Problems |
title_full |
A New Global Optimization Algorithm for Solving a Class of Nonconvex Programming Problems |
title_fullStr |
A New Global Optimization Algorithm for Solving a Class of Nonconvex Programming Problems |
title_full_unstemmed |
A New Global Optimization Algorithm for Solving a Class of Nonconvex Programming Problems |
title_sort |
new global optimization algorithm for solving a class of nonconvex programming problems |
publisher |
Hindawi Limited |
series |
Journal of Applied Mathematics |
issn |
1110-757X 1687-0042 |
publishDate |
2014-01-01 |
description |
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. |
url |
http://dx.doi.org/10.1155/2014/697321 |
work_keys_str_mv |
AT xuegangzhou anewglobaloptimizationalgorithmforsolvingaclassofnonconvexprogrammingproblems AT bingyuancao anewglobaloptimizationalgorithmforsolvingaclassofnonconvexprogrammingproblems AT xuegangzhou newglobaloptimizationalgorithmforsolvingaclassofnonconvexprogrammingproblems AT bingyuancao newglobaloptimizationalgorithmforsolvingaclassofnonconvexprogrammingproblems |
_version_ |
1725912212491468800 |