On nonsmooth robust multiobjective optimization under generalized convexity with applications to portfolio optimization

•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 uncerta...

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Veröffentlicht in:European journal of operational research Jg. 265; H. 1; S. 39 - 48
Hauptverfasser: Fakhar, Majid, Mahyarinia, Mohammad Reza, Zafarani, Jafar
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 16.02.2018
Schlagworte:
Generalized convexity
Nonsmooth saddle-point theorem
Optimality condition
Robust cardinality/mean-variance model
Robustness and sensitivity analysis
Nonsmooth saddle-point theorem
Optimality condition
Robust cardinality/mean-variance model
Robustness and sensitivity analysis
Generalized convexity
ISSN:0377-2217, 1872-6860
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Zusammenfassung:•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.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2017.08.003