Abstract:

The recent Wolfe-like conditions for the line-search quasi-Newton methods for unconstrained optimization will be analyzed. These conditions are used to modify the quasi-Newton updating formulae so that the positive definiteness of the Hessian approximations of the objective function is maintained without enforcing the Wolfe conditions. Numerical experiments, particularly those related to the well-known quasi-Newton BFGS and DFP methods and their modified self-scaling algorithms, will be described. It will be shown that combining both self-scaling and Wolf-like techniques in a sense to be defined is desirable for modifying several quasi-Newton methods. The useful effect of these techniques will be shown on a large number of standard test problems.