A MODIFIED BFGS FORMULA MAINTAINING POSITIVE DEFINITENESS WITH ARMIJO-GOLDSTEIN STEPLENGTHS  

作　　者：I. D. Coope C. J. Price 

出　　处：《Journal of Computational Mathematics》1995年第2期156-160,共5页计算数学（英文）

摘　　要：The line search subproblem in unconstrained optimization is concerned with finding an acceptable steplength satisfying certain standard conditions. The con-ditions proposed in the early work of Armijo and Goldstein are sometimes replaced by those recommended by Wolf e because these latter conditions automatically allow positive definiteness of some popular quasi-Newton updates to be maintained.It is shown that a slightly modified form of quasi-Newton update allows positive definiteness to be maintained even if line searches based on the Armijo-Goldsteinconditions are used.The line search subproblem in unconstrained optimization is concerned with finding an acceptable steplength satisfying certain standard conditions. The con-ditions proposed in the early work of Armijo and Goldstein are sometimes replaced by those recommended by Wolf e because these latter conditions automatically allow positive definiteness of some popular quasi-Newton updates to be maintained.It is shown that a slightly modified form of quasi-Newton update allows positive definiteness to be maintained even if line searches based on the Armijo-Goldsteinconditions are used.

关 键 词：DEFINITENESS Quadratic functions 

分 类 号：O242[理学—计算数学]