Singer I. Abstract convex analysis

Wiley, 1997. — 517 p.
The present book contains an exhaustive survey of the state-of-the-art in contemporary abstract convex analysis. In this book the reader can find a presentation of several approaches to abstract convexity and comparisons between them. Also presented are results concerning abstract convex sets and functions, abstract quasiconvex functions and related notions of subdifferentiability. Various types of abstract duality and conjugations are discussed in detail. The book also contains some new contributions by the author which have not previously been published. Many examples are given that help the reader to better understand the main concepts and techniques being developed.
The author mentions some applications of abstract convexity to optimization theory which will hopefully be the focus of a future contribution.