B-FORM OF THE DAVIDON–FLETCHER–POWELL METHOD

A special form (B-form) of methods of Quasi-Newton type is discussed, which makes it easy to interpret these methods as gradient in appropriately transformed argument space. B-form of the Davidon–Fletcher–Powell method is given and compared with r-algorithms. To minimize smooth convex functions, a gradient method with space transformation is built, combining properties of both quasi-Newtonian methods and r-algorithms. Possible schemes of this type of methods for minimizing non-smooth convex functions are discussed.