Mohebi, Hossein 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)].For the entire collection see [Zbl 1078.90003]. Reviewer: S. S. Kutateladze (Novosibirsk) Cited in 15 Documents MSC: 90C48 Programming in abstract spaces 52A01 Axiomatic and generalized convexity Keywords:abstract convexity; topical function Citations:Zbl 0985.90074 PDF BibTeX XML Cite \textit{H. Mohebi}, Appl. Optim. 99, 343--361 (2005; Zbl 1124.90048) OpenURL