The optimality conditions for generalized minimax programming

In this paper, we first weaken some assumptions in Jiao et al. (2005) [9] and discuss the continuity and the directional differentiability of the objective function. Furthermore, we investigate the optimality conditions for unconstrained and constrained generalized minimax programming. These optimality conditions are mixed ones that include different conditions at different directions, which is suitable for the non-differentiable objective function. For constrained problem we exploit two kinds of analysis methods to obtain some different optimality conditions. Moreover, we show these optimality conditions by some examples.