On nonsmooth robust multiobjective optimization under generalized convexity with applications to portfolio optimization - Fakhar, Majid; Mahyarinia, Mohammad Reza; Zafarani, Jafar (European journal of operational research, 2018)
•A new concept of generalized convexity at a given point for a family of real-valued functions is introduced and its application in portfolio optimization is given.•A nonsmooth sufficient optimality condition for robust (weakly) efficient solutions is obtained.•A robust duality theory for an uncertain multiobjective optimization is deduced.•A Mond–Weir type duality for an uncertain multiobjective optimization is given.•Existence for a new notion of the saddle-point is obtained. We introduce a new concept of generalized convexity at a given point for a family of real-valued functions and deduce nonsmooth sufficient optimality conditions for robust (weakly) efficient solutions. In addition, we present a robust duality theory and Mond–Weir type duality for an uncertain multiobjective optimization problem. Furthermore, some nonsmooth saddle-point theorems are obtained under our generalized convexity assumption. Finally we show the viability of our new concept of generalized convexity for robust optimization and portfolio optimization.