Annals of Operations Research

, Volume 244, Issue 2, pp 603–617 | Cite as

On second order duality of minimax fractional programming with square root term involving generalized B-(pr)-invex functions

Original Research

Abstract

The advantage of second-order duality is that if a feasible point of the primal is given and first-order duality conditions are not applicable (infeasible), then we may use second-order duality to provide a lower bound for the value of primal problem. Consequently, it is quite interesting to discuss the duality results for the case of second order. Thus, we focus our study on a discussion of duality relationships of a minimax fractional programming problem under the assumptions of second order B-(pr)-invexity. Weak, strong and strict converse duality theorems are established in order to relate the primal and dual problems under the assumptions. An example of a non trivial function has been given to show the existence of second order B-(pr)-invex functions.

Keywords

Minimax programming Fractional programming Nondifferentiable programming Second-order duality B-\((p , r)\)-invexity 

Notes

Acknowledgments

The research of Dr. Vikas Sharma is supported by Thapar University, Patiala under Seed Money Project no. TU/DORSP/57/581. He gratefully acknowledges the support provided by the Thapar University to carry out this research.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.School of MathematicsThapar UniversityPatialaIndia

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