Higher-Order Efficiency Conditions for Continuously Directional Differentiable Vector Equilibrium Problem with Constraints

In this paper, we give optimality conditions of higher-order for a continuously directional differentiable vector equilibrium problem with constraints. First, we obtain some important characterizations and existence results for a m -times continuously directional differentiable function( m is a positive integer number). Second, as an application, we provide some higher-order Karush–Kuhn–Tucker necessary optimality conditions for efficiency. Finally, some higher-order sufficient optimality conditions, which are very close to the higher-order Karush–Kuhn–Tucker necessary optimality conditions, are presented as well. Some illustrative examples are also given.