Research of Solving Bound Constrained Optimization of Nonlinear Programming with Orthogonal Design
Received date: 2002-09-10
Revised date: 2002-10-15
Online published: 2003-05-10
给出了以正交设计原理为基础的两种方法--正交表法和加点正交表法,求解非线性规划的区间约束最优化问题。方法不要求目标函数可导,不依赖于初始点,计算速度快,算法简单,容易编成程序在计算机上执行。用检验考题对算法进行了验证,并进行了分析和探讨
关键词： 正交设计; 正交表; 非线性规划区间约束最优化问题
王玉枝 , 张建方 . 用正交设计方法求解非线性规划的区间约束最优化问题[J]. 中国科学院大学学报, 2003 , 20(3) : 290 -295 . DOI: 10.7523/j.issn.2095-6134.2003.3.005
Introduces two methods called orthogonal array method and adding points orthogonal array method, which are based on the orthogonal design to solve bound constrained optimization of nonlinear programming. Methods are independent of the init ial points; the objective function need not be differentiable. Algorithms are simple and easy to be programed for running on a computer, and the running time is satisfactory. Some discussions are also given for a number of test ing problems.
[1] A Friedlander, J M Martinez, S A Santos. A New Trust Region Algorithm for Bound ConstrainedM-i nimization. Appl Math Opt im, 1994, 30: 235~266
[2] Fred J Hickernell, Yuan Ya-Xiang. A Simple Mult istart Algorithm for Global Optimization. Operat ional Research Transaction ( in Chinese), 1997, 2( 1) : 1~ 12
[3] 袁亚湘. 非线性规划数值方法. 上海: 上海科学技术出版社, 1992
[4] D M 希梅尔布劳. 实用非线性规划. 北京: 科学出版社, 1981
[5] Robert Michael Lewis, Virginia Torczon. Pattern Search Algorithms for Bound ConstrainedMinimizat ion. SIAMJ OPTIM, 1999, 9( 4) : 1082~ 1099
[6] MaryBranch, Thomas F Coleman,Li Yu-Ying.A Subspace, Interior and Conjugat e Gradient Method for Large-scale Bound-Const rained Minimizationproblems. SIAMJ SCI COMPUT, 1999, 21(1) : 1~ 23
[7] Matthias Heinkenschliss, Michael Ulbrich, Stefan Ulbrich. Superlinear and Quadratic Convergengence of Affine-Scaling Interior-Point Newt onMethodsfor Problems w ith Simple Bounds without St rict Complementarity Assumption. Math Program, 1999, 86( 3) : 615~ 635
[8] 中国现场统计研究会三次设计组, 全国总工会电教中心编著. 正交法和三次试验设计. 北京: 科学出版社, 1985
[9] 中国现场统计研究会最优化组编印. 正交表优化法汇编. 1987
[10] 张里千, 张建方. 多因素最优化的重大突破( 上, 下). 数理统计与管理, 1998, 17( 1) : 31~ 37; 1998, 17( 2) : 46~ 52
[11] 中国现场统计研究会三次设计组编著. 可计算性项目的三次设计. 北京: 北京大学出版社, 1985
[12] 陆 茵, 吕德伟. 串釜式反应精馏的非平衡级模型模拟. 宁波大学学报( 理工版), 1999, l (12) : 33~ 39
[13] 最优化与正交法交流会论文集. 1993
[14] 任露泉. 试验优化设计与分析. 吉林: 吉林科学技术出版社, 2001
[15] 张里千. 交互作用和多因素最优化. 数理统计与管理, 1991, 10( 3) : 28~ 35
[16] 余 俊, 周 济. 优化方法程序库OPB- 1) ) ) 原理及使用说明. 北京: 机械工业出版社, 1989
/
| 〈 |
|
〉 |
