| CONVEXIFICATION AND CONCAVIFICATION METHODS FOR SOME GLOBAL OPTIMIZATION PROBLEMS |
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| 作者姓名： | WUZhiyou ZHANGLiansheng BAIFusheng YANGXinmin |
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| 作者单位： | WU Zhiyou(School of Mathematics and Computer Science，Chongqing Normal University，Chongqing 400047; Department of Mathematics，Shanghai University，Shanghai 200436，China) ZHANG Liansheng(Department of Mathematics，Shanghai University，Shanghai 200436，China) BAI Fusheng(Institute of Mathematics，Fudan University，Shanghai 200433，China) YANG Xinmin(Department of Mathematics and Computer Science，Chongqing Normal University，Chongqing 400047，China) |
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| 基金项目： | This research is supported by the National Natural Science Foundation of China(Grant 10271073). |
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| 摘 要： | In this paper, firstly, we propose several convexification and concavification transformations to convert a strictly monotone function into a convex or concave function, then we propose several convexification and concavification transformations to convert a non-convex and non-concave objective function into a convex or concave function in the programming problems with convex or concave constraint functions, and propose several convexification and concavification transformations to convert a non-monotone objective function into a convex or concave function in some programming problems with strictly monotone constraint functions. Finally, we prove that the original programming problem can be converted into an equivalent concave minimization problem, or reverse convex programming problem or canonical D.C. programming problem. Then the global optimal solution of the original problem can be obtained by solving the converted concave minimization problem, or reverse convex programming problem or canonical D.C
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| 关 键 词： | 全局最优解 凹极小值 反转凸面程序 D.C.程序设计 凸化 凹化 严格单调函数 |
CONVEXIFICATION AND CONCAVIFICATION METHODS FOR SOME GLOBAL OPTIMIZATION PROBLEMS |
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| WUZhiyou ZHANGLiansheng BAIFusheng YANGXinmin.CONVEXIFICATION AND CONCAVIFICATION METHODS FOR SOME GLOBAL OPTIMIZATION PROBLEMS[J].Journal of Systems Science and Complexity,2004,17(3):421-436. |
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| Authors: | WU Zhiyou |
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| Abstract: | In this paper, firstly, we propose several convexification and concavification transformations to convert a strictly monotone function into a convex or concave function, then we propose several convexification and concavification transformations to convert a non-convex and non-concave objective function into a convex or concave function in the programming problems with convex or concave constraint functions, and propose several convexification and concavification transformations to convert a non-monotone objective function into a convex or concave function in some programming problems with strictly monotone constraint functions. Finally, we prove that the original programming problem can be converted into an equivalent concave minimization problem, or reverse convex programming problem or canonical D.C. programming problem. Then the global optimal solution of the original problem can be obtained by solving the converted concave minimization problem, or reverse convex programming problem or canonical D.C. programming problem using the existing algorithms about them. |
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| Keywords: | Global optimal solution concave minimization reverse convex programming problem D C programming problem convexification concavification |
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