A class of nonconvex functions and mathematical programming

Weir, Terence; Jeyakumar, V.

doi:10.1017/s0004972700027441

Cited by 114 publications

(52 citation statements)

References 18 publications

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“…, }. [20] and Weir and Jeyakumar [21]). The function ℎ is called preinvex on if, for all , ∈ , there exists a vector function such that ∀ ∈ [0, 1], + ( , ) ∈ , one has…”

Section: Preliminaries and Definitionsmentioning

confidence: 97%

Sufficiency and Duality in Nonsmooth Multiobjective Programming Problem under Generalized Univex Functions

Kharbanda

Agarwal

Sinha

2014

ISRN Applied Mathematics

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We consider a nonsmooth multiobjective programming problem where the functions involved are nondifferentiable. The class of univex functions is generalized to a far wider class of ( , , , )--V-type I univex functions. Then, through various nontrivial examples, we illustrate that the class introduced is new and extends several known classes existing in the literature. Based upon these generalized functions, Karush-Kuhn-Tucker type sufficient optimality conditions are established. Further, we derive weak, strong, converse, and strict converse duality theorems for Mond-Weir type multiobjective dual program.

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“…, }. [20] and Weir and Jeyakumar [21]). The function ℎ is called preinvex on if, for all , ∈ , there exists a vector function such that ∀ ∈ [0, 1], + ( , ) ∈ , one has…”

Section: Preliminaries and Definitionsmentioning

confidence: 97%

Sufficiency and Duality in Nonsmooth Multiobjective Programming Problem under Generalized Univex Functions

Kharbanda

Agarwal

Sinha

2014

ISRN Applied Mathematics

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“…For an example in [13], we consider the function f : R → R defined by f (x) = −|x|, then f , instead of a convex function, is a pre-invex function with η given by…”

Section: Definition 22 a Set C ⊆ X Is Said To Be Invex If There Exismentioning

confidence: 99%

On duality theory for non-convex semidefinite programming

Sun

Sampaio

2011

Ann Oper Res

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In this paper, with the help of convex-like function, we discuss the duality theory for nonconvex semidefinite programming. Our contributions are: duality theory for the general nonconvex semidefinite programming when Slater's condition holds; perfect duality for a special case of the nonconvex semidefinite programming for which Slater's condition fails. We point out that the results of [2] can be regarded as a special case of our result.Mathematics Subject Classifications: 65K05, 90C22, 90C26,

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“…and by (14), (ii) The space V is infinite dimensional, int conv(K y ) = ∅, and int conv(K y ) ∩ H = ∅.…”

Section: From Lemma 52 It Is Obtained Thatmentioning

confidence: 99%

On Convex Generalized Systems

Mastroeni

Rapcsák

2000

Journal of Optimization Theory and Applications

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A class of nonconvex functions and mathematical programming

Abstract: A class of functions, called pre-invex, is defined. These functions are more general than convex functions and when differentiable are invex. Optimality conditions and duality theorems are given for both scalar-valued and vector-valued programs involving pre-invex functions.

Cited by 114 publications

References 18 publications

Sufficiency and Duality in Nonsmooth Multiobjective Programming Problem under Generalized Univex Functions

Sufficiency and Duality in Nonsmooth Multiobjective Programming Problem under Generalized Univex Functions

On duality theory for non-convex semidefinite programming

On Convex Generalized Systems

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