A New Duality Principle and a Related Convex Dual Formulation Through a D.C. Approach for Non-Convex Variational Optimization
Fabio Botelho, Fabio Botelho · 2025
This article develops a duality principle and respective convex dual formulation 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 suitable for a large class of similar models in the calculus of variations.