Due to its simplicity and efficiency,the Barzilai and Borwein(BB)gradi-ent method has received various attentions in different fields.This paper presents a new analysis of the BB method for two-dimensional strictly co...Due to its simplicity and efficiency,the Barzilai and Borwein(BB)gradi-ent method has received various attentions in different fields.This paper presents a new analysis of the BB method for two-dimensional strictly convex quadratic func-tions.The analysis begins with the assumption that the gradient norms at the first two iterations are fixed.We show that there is a superlinear convergence step in at most three consecutive steps.Meanwhile,we provide a better convergence relation for the BB method.The influence of the starting point and the condition number to the convergence rate is comprehensively addressed.展开更多
基金This work was partly supported by the Chinese NSF grants(Nos.10831106 and 81173633)the CAS grant(No.kjcx-yw-s7-03)the China National Funds for Distinguished Young Scientists(No.11125107).
文摘Due to its simplicity and efficiency,the Barzilai and Borwein(BB)gradi-ent method has received various attentions in different fields.This paper presents a new analysis of the BB method for two-dimensional strictly convex quadratic func-tions.The analysis begins with the assumption that the gradient norms at the first two iterations are fixed.We show that there is a superlinear convergence step in at most three consecutive steps.Meanwhile,we provide a better convergence relation for the BB method.The influence of the starting point and the condition number to the convergence rate is comprehensively addressed.