A convex dual formulation for a large class of non-convex models in variational optimization

TL;DR

This paper introduces a convex dual formulation for many non-convex variational models, enabling more tractable analysis and solutions, demonstrated through a superconductivity application.

Contribution

It develops a general convex duality framework for non-convex variational models using functional and convex analysis, expanding the theoretical toolkit.

Findings

Established a convex dual formulation for a broad class of non-convex models.

Applied the duality principle to a Ginzburg-Landau system in superconductivity.

Provided foundational tools for analyzing complex variational problems.

Abstract

This short communication develops a convex dual variational formulation for a large class of models in variational optimization. The results are established through basic tools of functional analysis, convex analysis and duality theory. The main duality principle is developed as an application to a Ginzburg-Landau type system in superconductivity in the absence of a magnetic field.