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

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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}-invexity/η\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}-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).