| 求一类优化问题全局解的线性化方法 |
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| 引用本文： | 沈会焘,葛立,刘解放.求一类优化问题全局解的线性化方法[J].许昌学院学报,2007,26(5):18-21. |
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| 作者姓名： | 沈会焘 葛立 刘解放 |
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| 作者单位： | 1. 许昌学院,数学科学学院,河南,许昌,461000
2. 河南科技学院,数学系,河南,新乡,453003 |
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| 基金项目： | 河南省教育厅自然科学基金 |
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| 摘 要： | 对广泛应用于金融及经济等实际问题中的一类带有多乘积约束的线性规划问题提出一种全局优化算法.利用对数的性质和线性化技术,建立了问题的等价问题的松弛线性规划,并通过对可行域的细分以及一系列求解过程的讨论,从理论上证明了算法收敛到问题的全局最优解,并用数值结果验证了方法的可行性.
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| 关 键 词： | 全局优化 线性松弛 多乘积约束 分枝定界 |
| 文章编号： | 1671-9824（2007）05-0018-04 |
| 收稿时间： | 2006-03-22 |
| 修稿时间： | 2006年3月22日 |
Linearization Method for globally Solving A Kind of Optimization Problem |
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| SHEN Hui-tao,GE Li,LIU Jie-fang.Linearization Method for globally Solving A Kind of Optimization Problem[J].Journal of Xuchang University,2007,26(5):18-21. |
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| Authors: | SHEN Hui-tao GE Li LIU Jie-fang |
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| Institution: | 1. School of Mathematies and Science, Xuchang University, Xuchang 461000, China ; 2. Department of Mathematics, Henan Institute of Science and Technology, Xinxiang 453003, China |
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| Abstract: | In this paper a global optimization algorithm is proposed for some programming problem(P) with additional multiplicative constraints,which can be applied to finance and economics and so on.By utilizing the equivalent Problem(Q) of problem(P) and linearization technique for additional multiplicative constraints,a relaxation linear programming problem(Q1) about problem(Q) is established.Through the successive refinement of the linear relaxation of the feasible region of the objection function and the solutions of a series of(Q1),the proposed algorithm is proved to be convergent to the global minimum of problem(Q).And finally the numerical experiment result is given to illustrate the feasibility of the proposed algorithm. |
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| Keywords: | global optimization linear relaxation multiplicative constraints branch and bound |
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