On duality principles for non-convex variational models applied to a Ginzburg-Landau type equation

Abstract

This article develops a duality principle applicable to a large class of variational problems. Firstly, we apply the results to a Ginzburg-Landau type model. In a second step, we develop another duality principle and related primal dual variational formulation and such an approach includes optimality conditions which guarantee zero duality gap between the primal and dual formulations. We emphasize in both cases the dual variational formulations obtained have large regions of concavity about the critical points in question.