Method of H-hyperdifferential Descent

Abstract

In this paper H-hyperdifferentiable functions allowing a heterogeneous approximation are introduced. The H-hyperdifferentiability generalizes the well-known concept of hyperdifferentiability due to V. Demyanov using the concept of H-convexity proposed by A. Rubinov.

A necessary condition for a minimum of an H-hyperdifferentiable function is established. From the set of H-hyperdifferentiable functions a set of continuously H-hyperdifferentiable functions is singled out. Further we consider the problem of unconstrained minimization of a continuously H-hyperdifferentiable function. A constructive numerical method for finding stationary points is described.