Duality Principles and Numerical Procedures for a Large Class of Non-convex Models in the Calculus of Variations

Fabio Botelho

doi:10.20944/preprints202302.0051.v4

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preprints.org > computer science and mathematics > applied mathematics > doi: 10.20944/preprints202302.0051.v4

Preprint Article Version 4 Preserved in Portico This version is not peer-reviewed

Duality Principles and Numerical Procedures for a Large Class of Non-convex Models in the Calculus of Variations

Fabio Botelho

Version 1 : Received: 2 February 2023 / Approved: 3 February 2023 / Online: 3 February 2023 (02:35:00 CET)
Version 2 : Received: 8 February 2023 / Approved: 9 February 2023 / Online: 9 February 2023 (02:22:50 CET)
Version 3 : Received: 14 February 2023 / Approved: 15 February 2023 / Online: 15 February 2023 (04:11:16 CET)
Version 4 : Received: 16 February 2023 / Approved: 20 February 2023 / Online: 20 February 2023 (03:19:57 CET)
Version 5 : Received: 23 February 2023 / Approved: 23 February 2023 / Online: 23 February 2023 (03:37:43 CET)
Version 6 : Received: 26 February 2023 / Approved: 27 February 2023 / Online: 27 February 2023 (08:22:59 CET)
Version 7 : Received: 11 March 2023 / Approved: 13 March 2023 / Online: 13 March 2023 (04:16:53 CET)
Version 8 : Received: 27 March 2023 / Approved: 27 March 2023 / Online: 27 March 2023 (08:22:39 CEST)
Version 9 : Received: 3 April 2023 / Approved: 3 April 2023 / Online: 3 April 2023 (07:35:36 CEST)
Version 10 : Received: 7 April 2023 / Approved: 10 April 2023 / Online: 10 April 2023 (05:17:37 CEST)
Version 11 : Received: 22 April 2023 / Approved: 23 April 2023 / Online: 23 April 2023 (04:32:39 CEST)
Version 12 : Received: 28 April 2023 / Approved: 29 April 2023 / Online: 29 April 2023 (05:09:20 CEST)
Version 13 : Received: 16 May 2023 / Approved: 17 May 2023 / Online: 17 May 2023 (04:18:59 CEST)

How to cite: Botelho, F. Duality Principles and Numerical Procedures for a Large Class of Non-convex Models in the Calculus of Variations. Preprints.org 2023, 2023020051. https://doi.org/10.20944/preprints202302.0051.v4 Botelho, F. Duality Principles and Numerical Procedures for a Large Class of Non-convex Models in the Calculus of Variations. Preprints.org 2023, 2023020051. https://doi.org/10.20944/preprints202302.0051.v4

Cite as:

Botelho, F. Duality Principles and Numerical Procedures for a Large Class of Non-convex Models in the Calculus of Variations. Preprints.org 2023, 2023020051. https://doi.org/10.20944/preprints202302.0051.v4 Botelho, F. Duality Principles and Numerical Procedures for a Large Class of Non-convex Models in the Calculus of Variations. Preprints.org 2023, 2023020051. https://doi.org/10.20944/preprints202302.0051.v4

Abstract

This article develops duality principles and numerical results for a large class of non-convex variational models. The main results are based on fundamental tools of convex analysis, duality theory and calculus of variations. More specifically the approach is established for a class of non-convex functionals similar as those found in some models in phase transition. Finally, in the last section we present a concerning numerical example and the respective software.

Keywords

Duality theory; non-convex analysis; numerical method for a non-smooth model

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: 20 February 2023
Commenter: Fabio Botelho
Commenter's Conflict of Interests: Author

Comment: Dear Sir Editor

We have added a new section with an approximate convex formulation for a non-convex original one for a related model.

This new section includes a Theorem and replaces some of the final results concerning the previous version.

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