Abstract
In this paper we study the emerging area of abstract convexity. The theory of abstract convex functions and sets arises out of the properties of convex functions related to their global nature. One of the main applications of abstract convexity is global optimization. Apart from discussing the various fundamental facts about abstract convexity we also study quasiconvex functions in the light of abstract convexity. We further describe the surprising applications of the ideas of abstract convexity to the study of Hadamard type inequalities for quasiconvex functions.
The work of the first author was carried out by the Grant No. SAB1999-0184 of the Spanish Ministry of Education and Culture.
The work of the second author was carried out by the Grant No. SB99-B0771103B of the Spanish Ministry of Education and Culture.
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Rubinov, A., Dutta, J. (2005). Abstract Convexity. In: Hadjisavvas, N., Komlósi, S., Schaible, S. (eds) Handbook of Generalized Convexity and Generalized Monotonicity. Nonconvex Optimization and Its Applications, vol 76. Springer, New York, NY. https://doi.org/10.1007/0-387-23393-8_7
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DOI: https://doi.org/10.1007/0-387-23393-8_7
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