Projective dualities for quasiconvex problems

We study two dualities that can be applied to quasiconvex problems. They are conjugacies deduced from polarities. They are characterized by the polar sets of sublevel sets. We give some calculus rules for the associated subdifferentials and we relate the subdifferentials to known subdifferentials. We adapt the general duality schemes in terms of Lagrangians or in terms of perturbations to two specific problems. First a general mathematical programming problem and then a programming problem with linear constraints.