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 |
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16.02.2018
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| ISSN: | 0377-2217, 1872-6860 |
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| Abstract | •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. |
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| AbstractList | •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. |
| Author | Fakhar, Majid Mahyarinia, Mohammad Reza Zafarani, Jafar |
| Author_xml | – sequence: 1 givenname: Majid surname: Fakhar fullname: Fakhar, Majid email: fakhar@sci.ui.ac.ir organization: Department of Mathematics, University of Isfahan, Isfahan, Iran – sequence: 2 givenname: Mohammad Reza orcidid: 0000-0001-5200-6445 surname: Mahyarinia fullname: Mahyarinia, Mohammad Reza email: mahyarinia@iaukhsh.ac.ir organization: Department of Mathematics, University of Isfahan, Isfahan, Iran – sequence: 3 givenname: Jafar orcidid: 0000-0002-8893-4902 surname: Zafarani fullname: Zafarani, Jafar email: jzaf@zafarani.ir organization: Department of Mathematics, University of Isfahan, Isfahan, Iran |
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| Keywords | Nonsmooth saddle-point theorem Optimality condition Robust cardinality/mean-variance model Robustness and sensitivity analysis Generalized convexity |
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