| 一些约束规划问题的近似全局最优解 |
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| 引用本文： | 吴至友,张连生.一些约束规划问题的近似全局最优解[J].运筹学学报,2007,11(1):1-15. |
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| 作者姓名： | 吴至友 张连生 |
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| 作者单位： | 1. 重庆师范大学数学与计算机科学学院,重庆,400047
2. 上海大学数学系,上海,200444 |
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| 基金项目： | 国家自然科学基金;重庆市科研项目 |
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| 摘 要： | 首先将一个具有多个约束的规划问题转化为一个只有一个约束的规划问题,然后通过利用这个单约束的规划问题,对原来的多约束规划问题提出了一些凸化、凹化的方法,这样这些多约束的规划问题可以被转化为一些凹规划、反凸规划问题．最后,还证明了得到的凹规划和反凸规划的全局最优解就是原问题的近似全局最优解．
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| 关 键 词： | 运筹学 全局最优解 凹极小 反凸规划 凸化 凹化 |
| 修稿时间： | 2002-11-14 |
The Approximate Global Optimal Solution for Some Constrained Programming Problems |
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| Wu Zhiyou,Zhang Liansheng.The Approximate Global Optimal Solution for Some Constrained Programming Problems[J].OR Transactions,2007,11(1):1-15. |
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| Authors: | Wu Zhiyou Zhang Liansheng |
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| Institution: | School of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, China; Department of Mathematics, Shanghai University, Shanghai 200444, China |
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| Abstract: | Firstly,convert a programming problem with multiple constraints into a programming problem with single constraint.Secondly,several convexification and con- cavification transformations for the constrained problem with strictly monotone constraint functions are proposed according to the transformed problem with single constraint,then this constrained programming problem can be converted into a concave minimization or a reverse convex programming problem.Finally,prove that any global optimal solution of the converted concave minimization problem or reverse convex programming problem ob- tained by the existing algorithms is an approximate global optimal solution of the original problem. |
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| Keywords: | Operations research global optimal solution concave minimization reverse convex programming problem convexification concavification |
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