Generalized Directional Derivative of (h;φ)-Convex Function and its Properties

The concept of directional derivatives is particularly useful in the motivation and development of some optimality criteria and computational procedures in nonlinear programming.With the help of Ben-Tal generalized algebraic operations,a kind of generalized directional derivatves for (h,φ)-convex functions is defined,which is a generalization of directional derivatives for convex functions.The formula is given for calculating generalized directional derivative by using the directional derivative of convex functions.The concept of (h,φ)-differentiable functions is introduced.The relationship between (h,φ)-differential and generalized directional derivative is presented for a class of (h,φ)-convex and (h,φ)-differentiable functions.Finally,The subdifferential is characterized by utilizing the generalized directional derivative.