Global Optimization for the Sum of Concave-Convex Ratios Problem
This paper presents a branch and bound algorithm for globally solving the sum of concave-convex ratios problem (P) over a compact convex set. Firstly, the problem (P) is converted to an equivalent problem (P1). Then, the initial nonconvex programming problem is reduced to a sequence of convex progra...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/879739 |
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| _version_ | 1850209916917121024 |
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| author | XueGang Zhou JiHui Yang |
| author_facet | XueGang Zhou JiHui Yang |
| author_sort | XueGang Zhou |
| collection | DOAJ |
| description | This paper presents a branch and bound algorithm for globally solving the sum of concave-convex ratios problem (P) over a compact convex set. Firstly, the problem (P) is converted to an equivalent problem (P1). Then, the initial nonconvex programming problem is reduced to a sequence of convex programming problems by utilizing linearization technique. The proposed algorithm is convergent to a global optimal solution by means of the subsequent solutions of a series of convex programming problems. Some examples are given to illustrate the feasibility of the proposed algorithm. |
| format | Article |
| id | doaj-art-92672e28985344c3a268a824d4e35804 |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-92672e28985344c3a268a824d4e358042025-08-20T02:09:55ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/879739879739Global Optimization for the Sum of Concave-Convex Ratios ProblemXueGang Zhou0JiHui Yang1School of Mathematics and Information Science, Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong, Higher Education Institutes, Guangzhou University, Guangzhou, Guangdong 510006, ChinaCollege of Science, Shenyang Agricultural University, Shenyang, Liaoning 110866, ChinaThis paper presents a branch and bound algorithm for globally solving the sum of concave-convex ratios problem (P) over a compact convex set. Firstly, the problem (P) is converted to an equivalent problem (P1). Then, the initial nonconvex programming problem is reduced to a sequence of convex programming problems by utilizing linearization technique. The proposed algorithm is convergent to a global optimal solution by means of the subsequent solutions of a series of convex programming problems. Some examples are given to illustrate the feasibility of the proposed algorithm.http://dx.doi.org/10.1155/2014/879739 |
| spellingShingle | XueGang Zhou JiHui Yang Global Optimization for the Sum of Concave-Convex Ratios Problem Journal of Applied Mathematics |
| title | Global Optimization for the Sum of Concave-Convex Ratios Problem |
| title_full | Global Optimization for the Sum of Concave-Convex Ratios Problem |
| title_fullStr | Global Optimization for the Sum of Concave-Convex Ratios Problem |
| title_full_unstemmed | Global Optimization for the Sum of Concave-Convex Ratios Problem |
| title_short | Global Optimization for the Sum of Concave-Convex Ratios Problem |
| title_sort | global optimization for the sum of concave convex ratios problem |
| url | http://dx.doi.org/10.1155/2014/879739 |
| work_keys_str_mv | AT xuegangzhou globaloptimizationforthesumofconcaveconvexratiosproblem AT jihuiyang globaloptimizationforthesumofconcaveconvexratiosproblem |