A generalized upper dini-directional derivation in vector optimization

Abstract

In this paper, a set-valued generalized upper Dini-directional derivative is introduced for a locally lipschitz vector-valued function. Some properties, such as sum formula and chain rule, of this upper Dini-directional derivative are derived. This upper Dini-directional derivative is applied to characterize a cone-convex function and a vector subdifferential and to derive optimality conditions for a multi-objective optimization problem with a locally Lipschitz vector-valued objective function over a convex set.

Keywords:

• Lipschitz Vector-valued Function
• Upper Dini-directional Derivative
• Weak Subdifferential
• Optimality Condition