Optimality Conditions of the Approximate Efficiency for Nonsmooth Robust Multiobjective Fractional Semi-Infinite Optimization Problems
This paper is devoted to the investigation of optimality conditions and saddle point theorems for robust approximate quasi-weak efficient solutions for a nonsmooth uncertain multiobjective fractional semi-infinite optimization problem (NUMFP). Firstly, a necessary optimality condition is established...
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| Vydáno v: | Axioms Ročník 12; číslo 7; s. 635 |
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01.07.2023
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| Abstract | This paper is devoted to the investigation of optimality conditions and saddle point theorems for robust approximate quasi-weak efficient solutions for a nonsmooth uncertain multiobjective fractional semi-infinite optimization problem (NUMFP). Firstly, a necessary optimality condition is established by using the properties of the Gerstewitz’s function. Furthermore, a kind of approximate pseudo/quasi-convex function is defined for the problem (NUMFP), and under its assumption, a sufficient optimality condition is obtained. Finally, we introduce the notion of a robust approximate quasi-weak saddle point to the problem (NUMFP) and prove corresponding saddle point theorems. |
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| AbstractList | This paper is devoted to the investigation of optimality conditions and saddle point theorems for robust approximate quasi-weak efficient solutions for a nonsmooth uncertain multiobjective fractional semi-infinite optimization problem (NUMFP). Firstly, a necessary optimality condition is established by using the properties of the Gerstewitz’s function. Furthermore, a kind of approximate pseudo/quasi-convex function is defined for the problem (NUMFP), and under its assumption, a sufficient optimality condition is obtained. Finally, we introduce the notion of a robust approximate quasi-weak saddle point to the problem (NUMFP) and prove corresponding saddle point theorems. |
| Audience | Academic |
| Author | Gao, Liu Han, Wenyan Yu, Guolin |
| Author_xml | – sequence: 1 givenname: Liu surname: Gao fullname: Gao, Liu – sequence: 2 givenname: Guolin surname: Yu fullname: Yu, Guolin – sequence: 3 givenname: Wenyan surname: Han fullname: Han, Wenyan |
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| Cites_doi | 10.1016/j.ejor.2017.08.003 10.1007/978-3-642-21114-0_8 10.1007/BF00940478 10.1007/s10957-018-1437-8 10.2298/FIL1614649A 10.3934/jimo.2008.4.287 10.1007/s10288-022-00506-4 10.1007/s10203-017-0186-8 10.37193/CJM.2019.03.16 10.1080/02331934.2017.1393675 10.1515/9781400831050 10.1080/02331934.2020.1763990 10.1016/j.jmaa.2008.10.009 10.1080/02331934.2021.1969393 10.1007/s40840-023-01466-6 |
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| References | Chuong (ref_5) 2016; 44 Kuroiwa (ref_12) 2012; 40 Lee (ref_18) 2012; 1 Pham (ref_4) 2023; 46 Chen (ref_19) 2019; 265 Caristi (ref_14) 2017; 40 Gerth (ref_20) 1990; 67 ref_13 Kabgani (ref_15) 2018; 67 Han (ref_21) 2022; 71 Antczak (ref_7) 2017; 30 ref_22 Sun (ref_3) 2020; 69 Long (ref_11) 2017; 4 ref_16 Pan (ref_8) 2022; 1 ref_9 Kanzi (ref_2) 2009; 351 Mishra (ref_6) 2013; 16 Fakhar (ref_17) 2018; 265 Tung (ref_23) 2022; 21 Khantree (ref_1) 2019; 35 Han (ref_10) 2020; 2020 |
| References_xml | – volume: 265 start-page: 39 year: 2018 ident: ref_17 article-title: On nonsmooth robust multiobjective optimization under generalized convexity with applications to portfolio optimization publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2017.08.003 – volume: 1 start-page: 275 year: 2012 ident: ref_18 article-title: Optimality Conditions for Approximate Solutions of Convex Semi-Infinite Vector Optimization Problems publication-title: Recent Dev. Vector Optim. doi: 10.1007/978-3-642-21114-0_8 – volume: 67 start-page: 297 year: 1990 ident: ref_20 article-title: Nonconvex separation theorems and some applications in vector optimization publication-title: J. Optim. Theory Appl. doi: 10.1007/BF00940478 – volume: 1 start-page: 1 year: 2022 ident: ref_8 article-title: Optimality conditions for generalized convex nonsmooth uncertain multi-objective fractional programming publication-title: J. Oper. Res. Soc. – ident: ref_9 – volume: 265 start-page: 411 year: 2019 ident: ref_19 article-title: Optimality Conditions and Duality for Robust Nonsmooth Multiobjective Optimization Problems with Constraints publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-018-1437-8 – volume: 30 start-page: 3649 year: 2017 ident: ref_7 article-title: Sufficient optimality conditions for semi-infinite multiobjective fractional programming under (Φ,ρ)-V-invexity and generalized (Φ,ρ)-V-invexity publication-title: Filomat doi: 10.2298/FIL1614649A – volume: 4 start-page: 287 year: 2017 ident: ref_11 article-title: Optimality conditions, duality and saddle points for nondifferentiable multiobjective fractional programs publication-title: J. Ind. Manag. Optim. doi: 10.3934/jimo.2008.4.287 – volume: 21 start-page: 151 year: 2022 ident: ref_23 article-title: Constraint qualifications and optimality conditions for robust nonsmooth semi-infinite multiobjective optimization problems publication-title: 4OR doi: 10.1007/s10288-022-00506-4 – volume: 40 start-page: 103 year: 2017 ident: ref_14 article-title: Necessary conditions for nonsmooth multiobjective semi-infinite problems using Michel-Penot subdifferential publication-title: Decis. Econ. Financ. doi: 10.1007/s10203-017-0186-8 – volume: 35 start-page: 417 year: 2019 ident: ref_1 article-title: On quasi approximate solutions for nonsmooth robust semi-infinite optimization problems publication-title: Carpathian J. Math. doi: 10.37193/CJM.2019.03.16 – volume: 67 start-page: 217 year: 2018 ident: ref_15 article-title: Characterization of (weakly/properly/robust) efficient solutions in nonsmooth semi-infinite multiobjective optimization using convexificators publication-title: Optimization doi: 10.1080/02331934.2017.1393675 – ident: ref_16 – volume: 2020 start-page: 1 year: 2020 ident: ref_10 article-title: Optimality conditions for a nonsmooth uncertain multiobjective programming problem publication-title: Complexity – ident: ref_13 doi: 10.1515/9781400831050 – volume: 69 start-page: 2109 year: 2020 ident: ref_3 article-title: Robust approximate optimal solutions for nonlinear semi-infinite programming with uncertainty publication-title: Optimization doi: 10.1080/02331934.2020.1763990 – volume: 44 start-page: 260 year: 2016 ident: ref_5 article-title: Nondifferentiable fractional semi-infinite multiobjective optimization problems publication-title: Oper. Res. – volume: 16 start-page: 69 year: 2013 ident: ref_6 article-title: Optimality and duality for nonsmooth multiobjective fractional semi-infinite programming problem publication-title: Adv. Nonlinear Var. Inequalities – volume: 351 start-page: 170 year: 2009 ident: ref_2 article-title: Nonsmooth semi-infinite programming problems with mixed constraints publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2008.10.009 – volume: 40 start-page: 305 year: 2012 ident: ref_12 article-title: On robust multiobjective optimization publication-title: J. Nonlinear Convex. Anal. – volume: 71 start-page: 4819 year: 2022 ident: ref_21 article-title: Connectedness of the approximate solution sets for set optimization problems publication-title: Optimization doi: 10.1080/02331934.2021.1969393 – ident: ref_22 – volume: 46 start-page: 73 year: 2023 ident: ref_4 article-title: On Isolated/Properly Efficient Solutions in Nonsmooth Robust Semi-infinite Multiobjective Optimization publication-title: Bull. Malays. Math. Sci. Soc. doi: 10.1007/s40840-023-01466-6 |
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| SubjectTerms | approximate solution Euclidean space generalized convexity Mathematical optimization Mathematical research multiobjective semi-infinite optimization Multiple objective analysis optimality conditions Optimization Robustness saddle point Saddle points Theorems |
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| Title | Optimality Conditions of the Approximate Efficiency for Nonsmooth Robust Multiobjective Fractional Semi-Infinite Optimization Problems |
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