Preprint Article Version 25 Preserved in Portico This version is not peer-reviewed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

Fabio Botelho
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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)
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Version 7 : Received: 13 November 2022 / Approved: 14 November 2022 / Online: 14 November 2022 (03:43:45 CET)
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Version 13 : Received: 4 January 2023 / Approved: 4 January 2023 / Online: 4 January 2023 (06:38:00 CET)
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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, a related convex dual formulation and primal 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. Other applications include primal dual variational formulations for a Burger's type equation and a Navier-Stokes system. We emphasize the novelty here is that the first dual variational formulation developed is convex for a primal formulation which is originally non-convex. Finally, we also highlight the primal dual variational formulations presented have a large region of convexity around any of their critical points.

Keywords

convex dual variational formulations; duality principles for non-convex local and global primal optimization; Ginzburg-Landau type equation

Subject

Computer Science and Mathematics, Applied Mathematics

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Comments (1)

Comment 1
Received: 12 December 2023
Commenter: Fabio Botelho
Commenter's Conflict of Interests: Author
Comment: Dear Sir Editor

We have added a new final section 10.
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