Condition for global minimum through abstract convexity

Subdifferential calculus and separation theorems play a crucial role for applications of classical convex analysis to global optimization. More precisely, they allow the formulation of conditions (necessary or sufficient) for the global minimum of some convex optimization problems. The theory of abstract convexity generalizes ideas of convex analysis by using the notion of global supports and the global definition of subdifferential. In order to apply this theory to optimization, we need to extend subdifferential calculus and separation properties into the area of abstract convexity. This is the main objective of the present thesis. The work should be useful to professionals in generalized convexity and global optimization.