Mathematics > Optimization and Control
[Submitted on 18 Aug 2021 (v1), last revised 2 Oct 2022 (this version, v10)]
Title:Dual variational formulations for a large class of non-convex models in the calculus of variations
View PDFAbstract: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 part final sections, 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.
Submission history
From: Fabio Botelho Ph.D. [view email][v1] Wed, 18 Aug 2021 17:30:35 UTC (4 KB)
[v2] Wed, 3 Nov 2021 17:28:15 UTC (5 KB)
[v3] Fri, 31 Dec 2021 16:05:51 UTC (7 KB)
[v4] Sun, 20 Feb 2022 18:40:58 UTC (7 KB)
[v5] Thu, 3 Mar 2022 13:32:12 UTC (8 KB)
[v6] Thu, 28 Apr 2022 18:14:22 UTC (9 KB)
[v7] Mon, 4 Jul 2022 14:47:52 UTC (8 KB)
[v8] Thu, 4 Aug 2022 17:50:37 UTC (8 KB)
[v9] Wed, 31 Aug 2022 00:53:59 UTC (8 KB)
[v10] Sun, 2 Oct 2022 17:57:28 UTC (13 KB)
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