HS与PR共轭梯度算法的整体收敛性

GLOBAL CONVERGENCE PROPERTIES OF PR AND HS CONJUGATE GRADIENT METHOD FOR OPTIMIZATION

研究共轭梯度算法的整体收敛性，在放宽了的强Ｗｏｌｆｅ搜索（１８）、（１９）下证明了［１］中提出的修正ＨＳ共轭梯度算法的收敛性，在充分下降性条件下，βｋ＝ｍａｘβＨＳｋ，０｛｝时也具有整体收敛性，同时，βｋ＝ｍａｘ０，βＰＲｋ｛｝时，利用Ａｒｍｉｊｏ搜索和Ｇｏｌｄｓｔｅｉｎ搜索的共轭梯度法也具有整体收敛性．

In this paper, the global convergence properties of conjugate gradient methods are studied. Under the relax strong Wolfe linesearch, we study the global convergence of HS method by using sufficient descent condition and prove the global convergence of PR conjugate gradient method with Armijo or Goldstein linesearch is also established. Meanwhile the global convergence of a modified HS conjugate gradient method with general Wolfe linesearch without sufficient descent condition is proved.