Preprint Article Version 12 Preserved in Portico This version is not peer-reviewed

On Duality Principles and Related Convex Dual Formulations Suitable for Local and Global Non-Convex Variational Optimization

Version 1 : Received: 12 October 2022 / Approved: 14 October 2022 / Online: 14 October 2022 (09:57:59 CEST)
Version 2 : Received: 20 October 2022 / Approved: 20 October 2022 / Online: 20 October 2022 (10:58:57 CEST)
Version 3 : Received: 21 October 2022 / Approved: 24 October 2022 / Online: 24 October 2022 (12:25:44 CEST)
Version 4 : Received: 28 October 2022 / Approved: 31 October 2022 / Online: 31 October 2022 (10:20:26 CET)
Version 5 : Received: 1 November 2022 / Approved: 3 November 2022 / Online: 3 November 2022 (08:49:42 CET)
Version 6 : Received: 6 November 2022 / Approved: 7 November 2022 / Online: 7 November 2022 (14:37:49 CET)
Version 7 : Received: 13 November 2022 / Approved: 14 November 2022 / Online: 14 November 2022 (03:43:45 CET)
Version 8 : Received: 16 November 2022 / Approved: 18 November 2022 / Online: 18 November 2022 (10:46:15 CET)
Version 9 : Received: 24 November 2022 / Approved: 24 November 2022 / Online: 24 November 2022 (14:33:34 CET)
Version 10 : Received: 2 December 2022 / Approved: 2 December 2022 / Online: 2 December 2022 (13:45:33 CET)
Version 11 : Received: 27 December 2022 / Approved: 27 December 2022 / Online: 27 December 2022 (12:14:19 CET)
Version 12 : Received: 28 December 2022 / Approved: 29 December 2022 / Online: 29 December 2022 (15:00:02 CET)
Version 13 : Received: 4 January 2023 / Approved: 4 January 2023 / Online: 4 January 2023 (06:38:00 CET)
Version 14 : Received: 8 January 2023 / Approved: 9 January 2023 / Online: 9 January 2023 (06:19:11 CET)
Version 15 : Received: 18 May 2023 / Approved: 19 May 2023 / Online: 19 May 2023 (08:55:25 CEST)
Version 16 : Received: 20 May 2023 / Approved: 22 May 2023 / Online: 22 May 2023 (14:32:04 CEST)
Version 17 : Received: 24 May 2023 / Approved: 24 May 2023 / Online: 24 May 2023 (13:31:37 CEST)
Version 18 : Received: 27 May 2023 / Approved: 29 May 2023 / Online: 29 May 2023 (14:09:28 CEST)
Version 19 : Received: 2 June 2023 / Approved: 6 June 2023 / Online: 6 June 2023 (09:55:31 CEST)
Version 20 : Received: 22 July 2023 / Approved: 24 July 2023 / Online: 24 July 2023 (09:38:24 CEST)
Version 21 : Received: 25 September 2023 / Approved: 26 September 2023 / Online: 27 September 2023 (10:14:46 CEST)
Version 22 : Received: 27 September 2023 / Approved: 28 September 2023 / Online: 29 September 2023 (14:03:20 CEST)
Version 23 : Received: 30 September 2023 / Approved: 2 October 2023 / Online: 4 October 2023 (10:15:31 CEST)
Version 24 : Received: 9 October 2023 / Approved: 10 October 2023 / Online: 11 October 2023 (07:33:34 CEST)
Version 25 : Received: 12 December 2023 / Approved: 12 December 2023 / Online: 12 December 2023 (10:15:39 CET)
Version 26 : Received: 13 December 2023 / Approved: 13 December 2023 / Online: 13 December 2023 (13:17:57 CET)

A peer-reviewed article of this Preprint also exists.

Botelho, F.S. On Duality Principles and Related Convex Dual Formulations Suitable for Local and Global Non-Convex Variational Optimization. Nonlinear Engineering 2023, 12, doi:10.1515/nleng-2022-0343. Botelho, F.S. On Duality Principles and Related Convex Dual Formulations Suitable for Local and Global Non-Convex Variational Optimization. Nonlinear Engineering 2023, 12, doi:10.1515/nleng-2022-0343.

Abstract

This article develops duality principles and related convex dual formulations suitable for the local and global optimization of non-convex primal formulations for a large class of models in physics and engineering. The results are based on standard tools of functional analysis, calculus of variations and duality theory. In particular, we develop applications to a Ginzburg-Landau type equation.

Keywords

convex dual variational formulation; duality principle for non-convex local primal optimization; Ginzburg-Landau type equation

Subject

Computer Science and Mathematics, Applied Mathematics

Comments (1)

Comment 1
Received: 29 December 2022
Commenter: Fabio Botelho
Commenter's Conflict of Interests: Author
Comment: Dear Sir Editor

We have made some necessary corrections in the final section concerning the previous version v11.

We believe the article is now correct and ready to be submitted to a Journal.

About the so far  high number of versions, we thank so much the editor and the readers for their patience and understanding.
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