Generalized higher-order cone-convex functions and higher-order duality in vector optimization

S. K. Suneja (), Sunila Sharma () and Priyanka Yadav ()
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S. K. Suneja: University of Delhi
Sunila Sharma: University of Delhi
Priyanka Yadav: University of Delhi

Annals of Operations Research, 2018, vol. 269, issue 1, No 33, 709-725

Abstract: Abstract In this paper, we introduce a new class of higher-order cone-convex, $$(K_1, K_2)$$ ( K 1 , K 2 ) -pseudoconvex and quasiconvex functions which encapsulates several already known functions. Higher-order sufficient optimality conditions have been established for a vector optimization problem over cones by using these functions, under weaker conditions on multipliers as compared to other papers in this domain. Wolfe type and Mond–Weir type higher-order duals are formulated and corresponding duality results are established. A number of previously studied problems appear as special cases of our primal-dual models. In case of nonlinear programming problem, our higher-order duals reduce to the corresponding higher-order duals given by Mangasarian (J Math Anal Appl 51:607–620, 1975) and Mond and Zhang (Generalized convexity, generalized monotonicity: recent results. Kluwer, Dordrecht, pp 357–372, 1998).

Keywords: Vector optimization; Cones; Higher-order convexity; Higher-order duality (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10479-017-2470-y

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