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 ar...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.展开更多
文摘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.
