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求解非线性方程组的一种修正CD投影算法
供稿: 黎勇 时间: 2018-11-19 次数:

作者:黎勇

作者单位:百色学院数学与统计学院

摘要:为了提高求解大规模非线性方程组的算法效率,克服存储需求大、算法复杂等缺点,本文在经典CD共轭梯度法基础上提出一个新的搜索方向公式,并结合线搜索技术和投影技术,设计一种修正的CD共轭梯度算法。该算法优点:(1)能够在不依赖任何线搜索的情况下始终满足充分下降条件;(2)搜索方向具有信赖域性质;(3)在常规假设条件下具有全局收敛性。数值试验表明,新算法的数值表现总体上要优于经典CD算法。

基金:国家自然科学基金资助项目(11661001;11661009);

关键词:非线性方程组;共轭梯度法;投影技术;全局收敛性;

Abstract:In order to overcome the weaknesses of the large storage requirements and complex computation of other algorithms, and to improve the efficiency of algorithms for large-scale nonlinear equations, a new search direction formula was put forward based on the CD conjugate gradient method. Meanwhile, a CD conjugate gradient algorithm for nonlinear equations was modified based on the projection technique and the search approach. The new algorithm has following properties: ( 1) sufficient descent property without any line search; ( 2) features of a trust region; ( 3) the global convergence under the general assumption conditions. The new algirithmis more efficient than the normal CD conjugate gradient method.

DOI:10.16186/j.cnki.1673-9787.2018.06.23

分类号:O224;O241.7

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