Global and Superlinear Convergence of a Class of Scaled Variable Metric Methods.

This paper considers a class of variable metric methods for unconstrained minimization. The update formulas are such that the quasi-Newton equation is not necessarily satisfied. Under appropriate assumptions on the function to be minimized, each algorithm in this class converges globally and superlinearly. Many practical problems in operations research may be reduced to minimizing a function with or without constraints. By means of penalty functions and similar techniques a constrained minimization problem can be converted into a sequence of unconstraiend minimization problems.