Quasiconvex infimal convolution of positive functions

The infimal convolution has an important role in convex analysis. It is closely related to a polar of a convex function. The paper uses the definition of a quasiconvex infimal convolution to define the present polar which is related to the polars defined respectively by Crouzeix and Greenberg & Pierskalla. In this work, the paper will define its quasi-tangential and will end by an example: the ‘surrogate duality’.