Pseudoconvex function

This paper is devoted to the investigation of optimality conditions for approximate quasi-weakly efficient solutions to a class of nonsmooth Vector Equilibrium Problem (VEP) via convexificators. First, a necessary optimality condition for approximate quasi-weakly efficient solutions to problem (VEP) is presented by making use of the properties of convexificators. Second, the notion of approximate pseudoconvex function in the form of convexificators is introduced, and its existence is verified by a concrete example. Under the introduced generalized convexity assumption, a sufficient optimality condition for approximate quasi-weakly efficient solutions to problem (VEP) is also established. Finally, a scalar characterization for approximate quasi-weakly efficient solutions to problem (VEP) is obtained by taking advantage of Tammer’s function.

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Pseudoconvex Function

Encyclopedia of Operations Research and Management Science ◽

10.1007/978-1-4419-1153-7_200660 ◽

2013 ◽

pp. 1188-1188

Keyword(s):

Pseudoconvex Function

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Characterization of the extrema of a pseudoconvex function in terms of limiting and strong limiting subdifferential

International Mathematical Forum ◽

10.12988/imf.2007.07241 ◽

2007 ◽

Vol 2 ◽

pp. 2711-2718

Author(s):

S. Lahrech ◽

J. Hlal ◽

A. Ouahab ◽

A. Jaddar ◽

A. Mbarki

Keyword(s):

Limiting Subdifferential ◽

Pseudoconvex Function

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Wolfe Type Second Order Nondifferentiable Symmetric Duality in Multiobjective Programming over Cone with Generalized (K, F)-Convexity

ISRN Applied Mathematics ◽

10.1155/2014/687917 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10

Author(s):

A. K. Tripathy

Keyword(s):

Multiobjective Programming ◽

Second Order ◽

Mixed Integer ◽

Integer Programming Problem ◽

Symmetric Duality ◽

New Class ◽

Duality Results ◽

Pseudoconvex Function ◽

Root Term ◽

Mixed Integer Programming Problem

A new class of second order (K, F) pseudoconvex function is introduced with example. A pair of Wolfe type second order nondifferentiable symmetric dual programs over arbitrary cones with square root term is formulated. The duality results are established under second order (K, F) pseudoconvexity assumption. Also a Wolfe type second order minimax mixed integer programming problem is formulated and the symmetric duality results are established under second order (K, F) pseudoconvexity assumption.

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