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.
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