Complete Solutions to General Box-Constrained Global Optimization Problems
This paper presents a global optimization method for solving general nonlinear programming problems subjected to box constraints. Regardless of convexity or nonconvexity, by introducing a differential flow on the dual feasible space, a set of complete solutions to the original problem is obtained, a...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/478608 |
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| _version_ | 1832553270695952384 |
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| author | Dan Wu Youlin Shang |
| author_facet | Dan Wu Youlin Shang |
| author_sort | Dan Wu |
| collection | DOAJ |
| description | This paper presents a global optimization method for solving general nonlinear programming
problems subjected to box constraints. Regardless of convexity or nonconvexity, by introducing a
differential flow on the dual feasible space, a set of complete solutions to the original problem is obtained,
and criteria for global optimality and existence of solutions are given. Our theorems improve and
generalize recent known results in the canonical duality theory. Applications to a class of constrained
optimal control problems are discussed. Particularly, an analytical form of the optimal control is
expressed. Some examples are included to illustrate this new approach. |
| format | Article |
| id | doaj-art-8006bc362e8c402496435ba3379be950 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-8006bc362e8c402496435ba3379be9502025-02-03T05:54:29ZengWileyJournal of Applied Mathematics1110-757X1687-00422011-01-01201110.1155/2011/478608478608Complete Solutions to General Box-Constrained Global Optimization ProblemsDan Wu0Youlin Shang1Department of Mathematics, Henan University of Science and Technology, Luoyang 471003, ChinaDepartment of Mathematics, Henan University of Science and Technology, Luoyang 471003, ChinaThis paper presents a global optimization method for solving general nonlinear programming problems subjected to box constraints. Regardless of convexity or nonconvexity, by introducing a differential flow on the dual feasible space, a set of complete solutions to the original problem is obtained, and criteria for global optimality and existence of solutions are given. Our theorems improve and generalize recent known results in the canonical duality theory. Applications to a class of constrained optimal control problems are discussed. Particularly, an analytical form of the optimal control is expressed. Some examples are included to illustrate this new approach.http://dx.doi.org/10.1155/2011/478608 |
| spellingShingle | Dan Wu Youlin Shang Complete Solutions to General Box-Constrained Global Optimization Problems Journal of Applied Mathematics |
| title | Complete Solutions to General Box-Constrained Global Optimization Problems |
| title_full | Complete Solutions to General Box-Constrained Global Optimization Problems |
| title_fullStr | Complete Solutions to General Box-Constrained Global Optimization Problems |
| title_full_unstemmed | Complete Solutions to General Box-Constrained Global Optimization Problems |
| title_short | Complete Solutions to General Box-Constrained Global Optimization Problems |
| title_sort | complete solutions to general box constrained global optimization problems |
| url | http://dx.doi.org/10.1155/2011/478608 |
| work_keys_str_mv | AT danwu completesolutionstogeneralboxconstrainedglobaloptimizationproblems AT youlinshang completesolutionstogeneralboxconstrainedglobaloptimizationproblems |