曲线搜索的有关理论与数值方法

Relevant Theories and Numerical Methods of Curvilinear Search

英文关键词:optimization method munerical integration  curvilinear search.

中文摘要:

      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．

英文摘要:

      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.