Special Class of Second-Order Non-Differentiable Symmetric Duality Problems with ( G, ? f )-Pseudobonvexity Assumptions

Ramu Dubey, Lakshmi Narayan Mishra and Rifaqat Ali
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Ramu Dubey: Department of Mathematics, J.C. Bose University of Science and Technology, YMCA, Faridabad 121 006, India
Lakshmi Narayan Mishra: Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT) University, Vellore 632 014, India
Rifaqat Ali: Department of Mathematics, College of Science, King Khalid University, Abha 9004, Saudi Arabia

Mathematics, 2019, vol. 7, issue 8, 1-16

Abstract: In this paper, we introduce the various types of generalized invexities, i.e., ? f -invex/ ? f -pseudoinvex and ( G , ? f ) -bonvex/ ( G , ? f ) -pseudobonvex functions. Furthermore, we construct nontrivial numerical examples of ( G , ? f ) -bonvexity/ ( G , ? f ) -pseudobonvexity, which is neither ? f -bonvex/ ? f -pseudobonvex nor ? f -invex/ ? f -pseudoinvex with the same ? . Further, we formulate a pair of second-order non-differentiable symmetric dual models and prove the duality relations under ? f -invex/ ? f -pseudoinvex and ( G , ? f ) -bonvex/ ( G , ? f ) -pseudobonvex assumptions. Finally, we construct a nontrivial numerical example justifying the weak duality result presented in the paper.

Keywords: symmetric duality; second-order; non-differentiable; ( G , ? f )-invexity/( G , ? f )-pseudoinvexity; ( G , ? f )-bonvexity/( G , ? f )-pseudobonvexity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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