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曲线搜索的有关理论与数值方法
引用本文:隋允康,聂宇泉,陆贤英.曲线搜索的有关理论与数值方法[J].数学研究与评论,1996,16(1):51-56.
作者姓名:隋允康  聂宇泉  陆贤英
作者单位:大连理工大学工程力学研究所;大连理工大学工程力学研究所;江苏无锡江南大学
摘    要:统一表达了无约束优化问题下降曲线的常微分方程组.证明了两个常见的方程组实质上是参数不同的同一曲线.指出并证明了一种方程组是有利于数值计算的.本文还提出了两个算法一基于积分的搜索法和附加插值法.研究表明曲线寻优与累积迭代信息的策略可以提高优化算法的效率和稳定性.借助于对偶规划本方法对约束优化问题也获得了效率.

关 键 词:曲线搜索  无约束优化  最佳化  数值法
收稿时间:8/6/1993 12:00:00 AM

Relevant Theories and Numerical Methods of Curvilinear Search
Sui Yunkang,Nie Zhongquan and Lu Xianying.Relevant Theories and Numerical Methods of Curvilinear Search[J].Journal of Mathematical Research and Exposition,1996,16(1):51-56.
Authors:Sui Yunkang  Nie Zhongquan and Lu Xianying
Institution:Dalian University of Technology; 116024;Dalian University of Technology; 116024;Jiangnan University; Jiangsu Wuxi 214063
Abstract:Some various ordinary differenrial equations are uniformly expressed to describe descending curves of the nonconstrained optimization problem. Two common seen equations are proven to illustrate an identical curve which are with different parameters essentially. A kind of the equations is proposed and is proven to be available for the numerical calculation. We also propose two algorithms-the search based on integrations and the additional inerpolution. Investigations shows that strategies of the curvilinear search and rensing iterative information may increase the efficiency and the stability of optimization algorithms.
Keywords:optimization method munerical integration  curvilinear search  
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