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Verma, Khushboo; Mathur, Pankaj; Gulati, Tilak Raj

A new approach on mixed-type nondifferentiable higher-order symmetric duality. (English) Zbl 1438.90383

J. Oper. Res. Soc. China 7, No. 2, 321-335 (2019).
Summary: 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 \(\eta \)-invexity/\(\eta \)-pseudoinvexity assumptions. Self-duality is also discussed. Our results generalize some existing dual formulations which were discussed by R. P. Agarwal et al. [Abstr. Appl. Anal. 2011, Article ID 103597, 14 p. (2011; Zbl 1229.49033)], X. Chen [J. Math. Anal. Appl. 290, No. 2, 423–435 (2004; Zbl 1044.90055)], T. R. Gulati and S. K. Gupta [ibid. 310, No. 1, 247–253 (2005; Zbl 1079.90148); ibid. 329, No. 1, 229–237 (2007; Zbl 1122.90092)], T. R. Gulati and K. Verma [Filomat 28, No. 8, 1661–1674 (2014; Zbl 1474.90503)], S. H. Hou and X. M. Yang [J. Math. Anal. Appl. 255, No. 2, 491–498 (2001; Zbl 0986.90054)], K. Verma and T. R. Gulati [“Higher order symmetric duality using generalized invexity”, in: Proceeding of 3rd International Conference on Operations Research and Statistics (ORS) (2013); J. Appl. Math. Inform. 32, No. 1–2, 153–159 (2014; Zbl 1311.90173)].

MSC:

90C46 Optimality conditions and duality in mathematical programming
90C30 Nonlinear programming

Keywords:

higher-order dual model; symmetric duality; duality theorems; higher-order invexity; generalized invexity; self duality

Citations:

Zbl 1229.49033; Zbl 1044.90055; Zbl 1079.90148; Zbl 1122.90092; Zbl 0986.90054; Zbl 1311.90173; Zbl 1474.90503
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Full Text: DOI

References:

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