| 基于单纯形剖分确定非线性比式和问题全局解的新方法 |
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| 引用本文： | 汪春峰,刘三阳.基于单纯形剖分确定非线性比式和问题全局解的新方法[J].系统工程理论与实践,2013,33(3):742-747. |
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| 作者姓名： | 汪春峰 刘三阳 |
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| 作者单位： | 1. 河南师范大学 数学与信息科学学院, 新乡 453007;
2. 西安电子科技大学 理学院, 西安 710071 |
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| 基金项目： | 国家自然科学基金，河南师范大学博士科研启动课题 |
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| 摘 要： | 针对经济与金融中出现的一类特殊非线性比式和问题,给出一种基于单纯形剖分的全局优化算法. 在算法中, 通过构造初始单纯形, 以及使用凸包络理论, 提出了一个确定原问题最优值下界的新方法. 在确定下界的同时, 将会得到原问题的n+1可行解, 这些可行解可以用于上界的改善. 理论上证明了算法的收敛性, 数值算例表明算法是有效可行的.
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| 关 键 词： | 全局优化 分支定界 单纯形对分 比式和 |
| 收稿时间： | 2010-10-08 |
New method for solving nonlinear sum of ratios problem based on simplicial bisection |
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| WANG Chun-feng
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LIU San-yang.New method for solving nonlinear sum of ratios problem based on simplicial bisection[J].Systems Engineering —Theory & Practice,2013,33(3):742-747. |
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| Authors: | WANG Chun-feng LIU San-yang |
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| Institution: | 1. College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China;
2. School of Science, Xidian University, Xi'an 710071, China |
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| Abstract: | For solving a special class of nonlinear sum of ratios problem arised in economy and finance, a global optimization algorithm is presented based on simplicial bisection. In this algorithm, by constructing an initial simplex and using convex envelope theory, a new method to determine lower bound of the optimal value for the original problem is proposed. With the determination of the lower bound, n+1 feasible points of the original problem will be found, which can be used to improve upper bound. Convergence of the algorithm is shown and some numerical examples are given to illustrate the feasibility and effectiveness of the presented algorithm. |
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| Keywords: | global optimization branch and bound simplicial bisection sum of ratios |
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