Generalized higher-order cone-convex functions and higher-order duality in vector optimization

Suneja, Surjeet Kaur; Sharma, Sunila; Yadav, Priyanka

doi:10.1007/s10479-017-2470-y

Cited by 5 publications

(3 citation statements)

References 20 publications

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“…The quasi/pseudo-convexity is one of the ways to generalization of convexity problems. The higher-order cone-convex functions listed below were defined by Suneja et al (2018):…”

Section: Introductionmentioning

confidence: 99%

Generalized Second-Order G-Wolfe Type Fractional Symmetric Program and their Duality Relations under Generalized Assumptions

Kumar

et al. 2023

Int. j. math. eng. manag. sci.

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In this article, we formulate the concept of generalize bonvexity/pseudobonvexity functions. We formulate duality results for second-order fractional symmetric dual programs of G-Wolfe-type model. In the next section, we explain the duality theorems under generalize bonvexity/pseudobonvexity assumptions. We identify a function lying exclusively in the class of generalize pseudobonvex and not in class of generalize bonvex functions. Our results are more generalized several known results in the literature.

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“…The quasi/pseudo-convexity is one of the ways to generalization of convexity problems. The higher-order cone-convex functions listed below were defined by Suneja et al (2018):…”

Section: Introductionmentioning

confidence: 99%

Generalized Second-Order G-Wolfe Type Fractional Symmetric Program and their Duality Relations under Generalized Assumptions

Kumar

et al. 2023

Int. j. math. eng. manag. sci.

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“…Information envelopment analysis, charge programming, hazard analysis, and portfolio hypothesis are all applications of fractional programming (see, for example, Ying, 2012;Antczak, 2015;Khalil and Abdullah, 2018;Dubey and Mishra, 2019;Kaur and Sharma, 2022). Suneja et al (2018), introduced higher-order Schaible type dual model and derived duality theorems under cone convex and other related functions. Kapoor et al (2017), analysed the results of duality relationship of Wolfe and Mond-Weir type models by using higher-order cone-convex, ) , ( 21 K K pseudoconvexity/quasiconvexity assumptions.…”

Section: Introductionmentioning

confidence: 99%

Higher-Order Wolfe Type Symmetric Fractional Programming Problem Under Generalized Assumptions

Kumar

Alam

Dubey

2022

Int. j. math. eng. manag. sci.

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The Wolfe-type model over arbitrary cones is a new sort of model that we introduce in this article. We defend duality theorems under more generalized higher-order assumptions in the section after this. We identify a function that only belongs to the class of generalize higher order pseudoinvex functions, not the class of generalize higher order invex functions. In the last section, we added a conclusion for future prosecutions for the researchers. Additionally, compared to earlier results in the literature, all of the results in this research are more broadly applicable.

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“…The modeling of problems as (P) covers broad classes of various optimization problems such as conic vector optimization problems, (standard) multiobjective/vector optimization problems, multiobjective approximation problems [8,23,42], and many optimization problems manufactured in practical fields like engineering or economics and finance, Over the last couple of decades, issues related to optimality conditions and duality for (weakly) efficient solutions of the model problem (P) have been extensively investigated in the literature; see [1,2,7,8,23,31,32,36] and other references therein. For other results concerning on optimality conditions and duality in both smooth/nonsmooth multiobjective/vector optimization problems involving convex/generalized convex functions, we refer the readers to [3,5,6,24,25,38,41] and other references therein.…”

Section: Introductionmentioning

confidence: 99%

Approximate optimality and approximate duality in nonsmooth composite vector optimization

Sirichunwijit¹,

Wangkeeree²,

Sisarat³

2021

CJM

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This paper concentrates on studying a nonsmooth composite vector optimization problem (P for brevity). We employ a fuzzy necessary condition for approximate (weakly) efficient solutions of a nonconvex and nonsmooth cone constrained vector optimization problem established in [Choung, T. D. Approximate solutions in nonsmooth and nonconvex cone constrained vector optimization Ann. Oper. Res. (2020), https://doi.org/10.1007/s10479-020-03740-3.] and the a chain rule for generalized differentiation to provide a necessary condition which exhibited in a Fritz-John type for approximate (weakly) efficient solutions of P. Sufficient optimality conditions for approximate (weakly) efficient solutions to P are also provided by means of proposing the use of (strictly) approximately generalized convex composite vector functions with respect to a cone. Moreover, an approximate dual vector problem to P is given and strong and converse duality assertions for approximate (weakly) efficient solutions are proved.

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Generalized higher-order cone-convex functions and higher-order duality in vector optimization

Cited by 5 publications

References 20 publications

Generalized Second-Order G-Wolfe Type Fractional Symmetric Program and their Duality Relations under Generalized Assumptions

Generalized Second-Order G-Wolfe Type Fractional Symmetric Program and their Duality Relations under Generalized Assumptions

Higher-Order Wolfe Type Symmetric Fractional Programming Problem Under Generalized Assumptions

Approximate optimality and approximate duality in nonsmooth composite vector optimization

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