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

TL;DR

This paper develops duality principles for non-convex variational models, specifically applied to Ginzburg-Landau equations, providing primal-dual formulations with zero duality gap and regions of concavity near critical points.

Contribution

It introduces new duality principles for non-convex variational problems and derives primal-dual formulations with optimality conditions ensuring zero duality gap.

Findings

Duality principles applicable to Ginzburg-Landau models.

Primal-dual formulations with zero duality gap.

Regions of concavity around critical points.

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.