A Primal Dual Variational Formulation Suitable for a Large Class of Non-Convex Problems in Optimization

Abstract

This chapter develops a new primal dual variational formulation suitable for a large class of non-convex problems in the calculus of variations. It obtains results through basic tools of convex analysis, duality theory, the Legendre transform concept and the respective relations between the primal and dual variables. The chapter establishes the dual formulation for the primal variables, however with a large domain region of concavity about a critical point, which makes such a formulation very interesting from a numerical analysis point of view. It formally proves that there is no duality gap between the primal and dual formulations in a local extremal context.