Abstract
In the present paper we introduce the concept of univex sets, and define a new class of functions, called univex functions, on them. These functions unify the concepts of convexity, B-vexity, invexity and B-invexity. Some of their properties are proved and applications in nonlinear programming are discussed. Furthermore, generalized univex functions are also introduced and their relationships to univex functions and convex (generalized convex) functions are also discussed. Under appropiate assumptions of univexity, optimality conditions and duality results for Mond-Weir duality are established. In the end some suggestions for further research have been made.
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© 1994 Springer-Verlag Berlin Heidelberg
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Bector, C.R., Chandra, S., Gupta, S., Suneja, S.K. (1994). Univex sets, functions and univex nonlinear programming. In: Komlósi, S., Rapcsák, T., Schaible, S. (eds) Generalized Convexity. Lecture Notes in Economics and Mathematical Systems, vol 405. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46802-5_1
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DOI: https://doi.org/10.1007/978-3-642-46802-5_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57624-2
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