A Duality Principle and a Convex Dual Formulation Including a Numerical Example for a Related Optimality Criterion and Some More New Developments

This article develops a duality principle through a D.C. approach applicable to some originally non-convex primal variational formulations. More specifically, in a first step, we develop applications to a Ginzburg-Landau type equation. The results are obtained through basic tools of functional analysis, calculus of variations, duality and optimization theory in infinite dimensional spaces. It is worth emphasizing we have obtained a convex dual variational formulation which may be applied to a large class of similar models in the calculus of variations.