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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Bibliographic Details
Published in:European journal of operational research Vol. 265; no. 1; pp. 39 - 48
Main Authors: Fakhar, Majid, Mahyarinia, Mohammad Reza, Zafarani, Jafar
Format: Journal Article
Language:English
Published: Elsevier B.V 16.02.2018
Subjects:
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
Online Access:Get full text
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Summary:•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