On accelerating Newton's method based on a conic model

Abstract

We discuss a method that utilizes a conic approximating model function and second-order derivative information, in much the same way that Newton's method utilizes a quadratic approximating model function and second-order information. It defines a search direction as the Newton direction augmented by a multiple of the preceding step, and thus resembles a preconditioned conjugate gradient iteration in a metric defined by the current Hessian matrix. Algorithmic implications of this interpretation are briefly explored.