Higher-order cone-pseudoconvex, quasiconvex and other related functions in vector optimization |
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Authors: | S K Suneja Pooja Louhan Meetu Bhatia Grover |
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Institution: | 1. Department of Mathematics, Miranda House, University of Delhi, New Delhi, 110 007, India 2. Department of Mathematics, University of Delhi, New Delhi, 110 007, India
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Abstract: | Recently Bhatia (Optim. Lett. doi:10.1007/s11590-010-0248-0, 2010) introduced higher-order cone-convex functions and used them to obtain higher-order sufficient optimality conditions and duality results for a vector optimization problem over cones. The concepts of higher-order (strongly) cone-pseudoconvex and cone-quasiconvex functions were also defined by Bhatia (Optim. Lett. doi:10.1007/s11590-010-0248-0, 2010). In this paper we introduce the notions of higher-order naturally cone-pseudoconvex, strictly cone-pseudoconvex and weakly cone-quasiconvex functions and study various interrelations between the above mentioned functions. Higher-order sufficient optimality conditions have been established by using these functions. Generalized Mond–Weir type higher-order dual is formulated and various duality results have been established under the conditions of higher-order strongly cone-pseudoconvexity and higher-order cone quasiconvexity. |
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