A New Approach on Mixed-Type Nondifferentiable Higher-Order Symmetric Duality

doi:10.1007/s40305-018-0213-7

Journal of the Operations Research Society of China ›› 2019, Vol. 7 ›› Issue (2): 321-335.doi: 10.1007/s40305-018-0213-7

Special Issue: Continuous Optimization

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A New Approach on Mixed-Type Nondifferentiable Higher-Order Symmetric Duality

Khushboo Verma¹, Pankaj Mathur¹, Tilak Raj Gulati²

1 Department of Mathematics and Astronomy, University of Lucknow, Lucknow 226001, India;
2 Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667, India

Received:2016-07-05 Revised:2017-11-09 Online:2019-06-30 Published:2019-06-30
Contact: Khushboo Verma, Pankaj Mathur, Tilak Raj Gulati E-mail:1986khushi@gmail.com;pankaj_mathur14@yahoo.co.in;trgulati@gmail.com
Supported by:
The research of Khushboo Verma was supported by the Department of Atomic Energy, Govt. of India, the NBHM Post-Doctoral Fellowship Program (No. 2/40 (31)/2015/RD-II/9474).

Abstract

Abstract: In this paper, a new mixed-type higher-order symmetric duality in scalar-objective programming is formulated. In the literature we have results either Wolfe or Mond-Weir-type dual or separately, while in this we have combined those results over one model. The weak, strong and converse duality theorems are proved for these programs under η-invexity/η-pseudoinvexity assumptions. Self-duality is also discussed. Our results generalize some existing dual formulations which were discussed by Agarwal et al. (Generalized second-order mixed symmetric duality in nondifferentiable mathematical programming. Abstr. Appl. Anal. 2011. https://doi.org/10.1155/2011/103597), Chen (Higher-order symmetric duality in nonlinear nondifferentiable programs), Gulati and Gupta (Wolfe type second order symmetric duality in nondifferentiable programming. J. Math. Anal. Appl. 310, 247-253, 2005, Higher order nondifferentiable symmetric duality with generalized F-convexity. J. Math. Anal. Appl. 329, 229-237, 2007), Gulati and Verma (Nondifferentiable higher order symmetric duality under invexity/generalized invexity. Filomat 28(8), 1661-1674, 2014), Hou and Yang (On second-order symmetric duality in nondifferentiable programming. J Math Anal Appl. 255, 488-491, 2001), Verma and Gulati (Higher order symmetric duality using generalized invexity. In:Proceeding of 3rd International Conference on Operations Research and Statistics (ORS). 2013. https://doi.org/10.5176/2251-1938_ORS13.16, Wolfe type higher order symmetric duality under invexity. J Appl Math Inform. 32, 153-159, 2014).

Key words: Higher-order dual model, Symmetric duality, Duality theorems, Higher-order invexity/generalized invexity, Self duality

CLC Number:

Khushboo Verma, Pankaj Mathur, Tilak Raj Gulati. A New Approach on Mixed-Type Nondifferentiable Higher-Order Symmetric Duality[J]. Journal of the Operations Research Society of China, 2019, 7(2): 321-335.

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References 18

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A New Approach on Mixed-Type Nondifferentiable Higher-Order Symmetric Duality

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