Sufficiency and duality in interval-valued variational programming

Ismail, Ahmad; Jayswal, Anurag; Al-Homidan, Suliman; Banerjee, Jonaki

doi:10.1007/s00521-017-3307-y

Cited by 26 publications

(11 citation statements)

References 22 publications

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“…Bector and Husain [16] extended the concept of duality used in vector optimization problem to variational problem. Thereafter, many researchers derived duality relations for multiobjective problem under generalized invexity assumptions [9,[16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

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On optimality and duality in interval-valued variational problem withB-(p,r)-invexity

Debnath

Pokharna

2021

RAIRO-Oper. Res.

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In this paper, we consider a class of interval-valued variational optimization problem. We extend the definition of B -( p,r )- invexity which was originally defined for scalar optimization problem to the interval-valued variational problem. The necessary and sufficient optimality conditions for the problem have been established under B -( p,r )-invexity assumptions. An application, showing utility of the sufficiency theorem in real-world problem, has also been provided. In addition to this, for an interval- optimization problem Mond-Weir and Wolfe type duals are presented and related duality theorems have been proved. Non-trivial examples verifying the results have also been presented throughout the paper.

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Section: Introductionmentioning

confidence: 99%

“…Zhang et al [27] derived various duality results for a multiobjective variational control problem with G-invexity. Very recently, Ahmad et al [17] studied sufficiency and duality for an interval-valued variational problem under invexity assumption.…”

Section: Introductionmentioning

confidence: 99%

On optimality and duality in interval-valued variational problem withB-(p,r)-invexity

Debnath

Pokharna

2021

RAIRO-Oper. Res.

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“…In 2016, Singh et al [33] proposed the concept of Pareto optimal solution for the interval-valued multi-objective programming problems. Many other researchers have also proposed optimality conditions and solution concepts for IOPs, see for instance [1,12,15,16,35] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Weak Sharp Minima for Interval-Valued Functions and its Primal-Dual Characterizations Using Generalized Hukuhara Subdifferentiability

Kumar

Ghosh

Kumar

2021

Preprint

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This article introduces the concept of weak sharp minima (WSM) for convex interval-valued functions (IVFs). To identify a set of WSM of a convex IVF, we provide its primal and dual characterizations. The primal characterization is given in terms of gHdirectional derivatives. On the other hand, to derive dual characterizations, we propose the notions of the support function of a subset of I(R) n and gH-subdifferentiability for convex IVFs. Further, we develop the required gH-subdifferential calculus for convex IVFs. Thereafter, by using the proposed gH-subdifferential calculus, we provide dual characterizations for the set of WSM of convex IVFs.

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Section: Introductionmentioning

confidence: 99%

Weak sharp minima for interval-valued functions and its primal-dual characterizations using generalized Hukuhara subdifferentiability

Kumar¹,

Ghosh²,

Kumar³

2021

Preprint

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This article introduces the concept of weak sharp minima (WSM) for convex intervalvalued functions (IVFs). To identify a set of WSM of a convex IVF, we provide its primal and dual characterizations. The primal characterization is given in terms of gH-directional derivatives. On the other hand, to derive dual characterizations, we propose the notions of the support function of a subset of I(R) n and gH-subdifferentiability for convex IVFs. Further, we develop the required gH-subdifferential calculus for convex IVFs. Thereafter, by using the proposed gH-subdifferential calculus, we provide dual characterizations for the set of WSM of convex IVFs.

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Sufficiency and duality in interval-valued variational programming

Cited by 26 publications

References 22 publications

On optimality and duality in interval-valued variational problem withB-(p,r)-invexity

On optimality and duality in interval-valued variational problem withB-(p,r)-invexity

Weak Sharp Minima for Interval-Valued Functions and its Primal-Dual Characterizations Using Generalized Hukuhara Subdifferentiability

Weak sharp minima for interval-valued functions and its primal-dual characterizations using generalized Hukuhara subdifferentiability

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