The theory of convex optimization has been constantly developing over the past 30 years. Most
recently many researchers have been studying more complicated classes of problems that still
can be studied by means of convex analysis so-called anticonvex and convex-anticonvex
optimizaton problems. This manuscript contains an exhaustive presentation of the duality for
these classes of problems and some of its generalization in the framework of abstract
convexity. This manuscript will be of great interest for experts in this and related fields.
