Cone convex and related functions in optimization over topological vector spaces

Cone convex and related functions in optimization over topological vector spaces

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Article ID: iaor20084122
Country: Singapore
Volume: 24
Issue: 6
Start Page Number: 741
End Page Number: 754
Publication Date: Dec 2007
Journal: Asia-Pacific Journal of Operational Research
Authors: ,
Keywords: duality
Abstract:

In this paper cone convex and related functions have been studied. The concept of cone semistrictly convex functions on topological vector spaces is introduced as a generalization of semistrictly convex functions. Certain properties of these functions have been established and their interrelations with cone convex and cone subconvex functions have been explored. Assuming the functions to be cone subconvex, sufficient optimality conditions are proved for a vector valued minimization problem over topological vector spaces, involving Gâteaux derivatives. A Mond–Weir type dual is associated and weak and strong duality results are proved.

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