On General Duality Principles for Non-Convex Variational Optimization with Applications to the Ginzburg-Landau System in Superconductivity

2018/04/17 by Fabio Botelho, Botelho, Fabio
Computer Science · Mathematics · #49K20 #49N15 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Spectral Theory in Mathematical Physics #math.OC #msc:49K20 #msc:49N15

paper · pdf · doi:10.48550/arxiv.1804.06283

32 pages, typos corrected, other results added

openalex publication_date 2018/04/17 · arxiv created 2018/10/10 · arxiv updated 2018/10/11 · openalex created_date 2018/10/26 · openalex updated_date 2026/07/28

Abstract

This article develops duality principles applicable to non-convex models in the calculus of variations. The results here developed are applied to Ginzburg-Landau type equations. For the first and second duality principles, through an optimality criterion developed for the dual formulations, we qualitatively classify the critical points of the primal and dual functionals in question. We formally prove there is no duality gap between the primal and dual formulations in a local extremal context. Finally, in the last sections, we present a global existence result, a duality principle and respective optimality conditions for the complex Ginzburg-Landau system in superconductivity in the presence of a magnetic field and concerning magnetic potential.

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