  Convexity is an important notion in non linear optimization theory as well as
in infinite dimensional functional analysis. As will be seen below, very simple
and powerful tools will be derived from elementary duality arguments (which are
byproducts of the Moreau-Fenchel transform and Hahn Banach Theorem). We will
emphasize on applications to a large range of variational problems. Some
arguments of measure theory will be skipped.
