Higher-Order Generalized InvexityAndStrict Minimizers In Vector Optimization Within Conic Spaces
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Abstract
Optimisation theory is a cornerstone of engineering and technology, providing essential tools and methodologies for enhancing performance, efficiency, and functionality across various applications. This paper delves into the vector optimisation problem within the context of cones, a critical area that underpins many advanced engineering and technological processes. To this aim, Higher order Kstrict minimizers and higher order strongly K-non smooth invex functions and its generalizations are defined for a vector optimization problem over cones and Kuhn Tucker type necessary optimality condition are established for a K-strict minimizers of higher order. Further, these K-strict minimizers of higher order are characterized via sufficient optimality conditions by utilizing the above functions. Finally a Mond-Weir type dual is formulated and corresponding duality results are obtained.