A survey of recent[1985-1995]advances in generalized convexity with applications to duality theory and optimality conditions

Convexity plays a very important role in various branches of mathematical, natural and social sciences. In an effort to extend existing results depending on convexity there has been a steady interest over the years towards its generalizations. Many excellent books, monographs and numerous articles have been written pursuing generalizations of the basic concepts, their characterizations. and studying properties under different conditions. The purpose of this contribution is to gather information on certain generalizations of convexity and their applications to duality theory and optimality conditions

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