| 求全局最优解的新算法 |
| |
| 引用本文： | 盛平兴,汤正诠.求全局最优解的新算法[J].应用数学与计算数学学报,2004,18(2):15-23. |
| |
| 作者姓名： | 盛平兴 汤正诠 |
| |
| 作者单位： | 上海大学理学院数学系,上海,200436 |
| |
| 摘 要： | 利用局部极大值点与动力系统的稳定奇点的对应性，计算代数方程的根、无约束极大值点、有约束极大值点、非线性规划解、及最小二乘解．我们采用了常微分方程数值解的Euler算法及网格初始点的循序迭代算法，并以具体的例子和程序说明创立的方法具有通用性，同时考虑了一些存在的问题以便在理论和算法上作进一步的改进。
|
| 关 键 词： | 极大值点 全局最优解 最小二乘解 代数方程 奇点 常微分方程 数值解 新算法 网格 约束 |
| 修稿时间： | 2004年1月8日 |
New Algorithm on Seeking Global Optimal Solutions |
| |
| Sheng Pingxing Tang Zhengquan.New Algorithm on Seeking Global Optimal Solutions[J].Communication on Applied Mathematics and Computation,2004,18(2):15-23. |
| |
| Authors: | Sheng Pingxing Tang Zhengquan |
| |
| Institution: | Sheng Pingxing Tang Zhengquan Department of Mathematics,College of Sciences,Shanghai University,Shanghai 200436,China |
| |
| Abstract: | The correspondence relation between local maximum points and the stable equilibria of the gradient dynamical system x= (?)f(x) is applied to build up specific algorithms in computing algebraic roots, unconstrained maximum points, constrained maximum points, solutions of nonlinear programming, and least square solutions. Euler algorithm of initial value problems of ODEs and net initial points are adopted in computing examples. It indicates the method possess generality, but many theoretical problems and computational problems can be pulled out to improve the method. |
| |
| Keywords: | extreme points of function stable equilibrium of dynamical systems algebraic roots constrained or unconstrained optimization nonlinear programming least square solutions Euler algorithm net initial points |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
