Dual Variational Formulations for a Large Class of Non-Convex Models in the Calculus of Variations

Autor:	Fabio Silva Botelho
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	duality principles non-convex optimization generalized method of lines Mathematics QA1-939
Zdroj:	Mathematics, Vol 11, Iss 1, p 63 (2022)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math11010063
Popis:	This article develops dual variational formulations 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. In the first section, we develop new general dual convex variational formulations, more specifically, dual formulations with a large region of convexity around the critical points, which are suitable for the non-convex optimization for a large class of models in physics and engineering. Finally, in the last section, we present some numerical results concerning the generalized method of lines applied to a Ginzburg–Landau-type equation.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/ae6b4933691c4ac782f2dcb5fe46b070 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
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