摘要
求解无约束优化问题的共轭梯度法,其搜索方向的下降性往往依赖于所采用的线性搜索.将提出一种修正的CD算法,其搜索方向d_k始终满足1-1/u≤(-g_k^Td_k)/(‖g_k‖~2)≤1+1/u(u>1),即算法在不依赖任何线性搜索的情况下能始终产生充分下降方向.同时,当采用精确线性搜索时,该修正的CD算法就是标准的CD共轭梯度法.在适当条件下,还证明了修正的CD算法在强Wolfe线性搜索下具有全局收敛性.最后,我们给出了相应的数值结果,说明了算法是一种有效的算法.
The conjugate gradient methods are welcome methods for solving optimization problems,but its descent property is always guaranteed by the line search used.In this paper,we take a little modification to the CD conjugate gradient method such that the direction generated by the modified method satisfies 1-1/u≤（-g_k^Td_k）/（‖gk‖~2）≤1 ＋1/u（u〉1）.This property depends neither on the line search used,nor on the convexity of the objective function.Moreover,if exact line search is used,the method reduces to the ordinary CD method.Under mild conditions,we prove that the modified CD method with strong Wolfe line search is globally convergent.At the end of this paper,we also present numerical results to show the efficiency of the proposed method.
出处
《数学的实践与认识》
北大核心
2016年第15期245-250,共6页
Mathematics in Practice and Theory
基金
云南省自然科学基金(2014FD053)
云南省教育厅科学研究基金(2013Y064)
