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Topical functions and their properties in a class of ordered Banach spaces. (English) Zbl 1124.90048
Jeyakumar, Vaithilingam (ed.) et al., Continuous optimization. Current trends and modern applications. New York, NY: Springer (ISBN 0-387-26769-7/hbk). Applied Optimization 99, 343-361 (2005).
The author abstracts the concept of a real topical function on an arithmetic space to the case when the domain of definition is a Banach space ordered by a normal cone. The preliminaries of the relevant conjugates and subdifferentials are discussed in terms of abstract convexity [see A. Rubinov, Abstract Convexity and Global Optimization. Nonconvex Optimization and Its Applications. 44. Dordrecht: Kluwer Academic Publishers (2000; Zbl 0985.90074)].
MSC:
90C48Programming in abstract spaces
52A01Axiomatic and generalized geometric convexity