ABSTRACT
The nonsmooth minmax programming problems have been the subject of intense investigation during the past few years. Due to their applications in a great variety of optimal decision making situations, these problems have been widely studied. Bhatia and Jain [25] derived sufficient optimality conditions for a general minmax programming problem under nondifferentiable pseudoconvexity assumptions using pseudoconvexity in terms of classical Dini derivatives. Further, Bhatia and Jain [25] introduced a dual in terms of Dini derivatives for a general minmax programming problem and established duality results. Mehra and Bhatia [182] proved optimality conditions and various duality results in the sense of Mond and Weir [207] for a static minmax programming problem in terms of the right derivatives of the functions involved with respect to the same arc. Studniarski and Taha [262] have derived first order necessary optimality conditions for nonsmooth static minmax programming problems. For further details and recent developments about optimality conditions and duality theorems for the nonsmooth minmax programming problems involving generalized convex functions, we refer to Kuk and Tanino [154], Mishra and Shukla [196], Zheng and Cheng [300], Yuan et al. [293], Antczak [6], Ho and Lai [107], Yuan and Liu [294], Mishra and Upadhyay [201], and the references cited therein.
