A Duality Principle and a Concerning Convex Dual Formulation Suitable for Non-convex Variational Optimization

Fabio Botelho

doi:10.20944/preprints202210.0116.v7

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preprints.org > computer science and mathematics > applied mathematics > doi: 10.20944/preprints202210.0116.v7

Preprint Article Version 7 Preserved in Portico This version is not peer-reviewed

A Duality Principle and a Concerning Convex Dual Formulation Suitable for Non-convex Variational Optimization

Fabio Botelho

Version 1 : Received: 6 October 2022 / Approved: 10 October 2022 / Online: 10 October 2022 (09:52:15 CEST)
Version 2 : Received: 11 October 2022 / Approved: 11 October 2022 / Online: 11 October 2022 (09:57:49 CEST)
Version 3 : Received: 19 November 2022 / Approved: 21 November 2022 / Online: 21 November 2022 (12:55:10 CET)
Version 4 : Received: 24 November 2022 / Approved: 24 November 2022 / Online: 24 November 2022 (14:34:07 CET)
Version 5 : Received: 2 December 2022 / Approved: 2 December 2022 / Online: 2 December 2022 (13:48:39 CET)
Version 6 : Received: 21 December 2022 / Approved: 21 December 2022 / Online: 21 December 2022 (13:07:06 CET)
Version 7 : Received: 23 December 2022 / Approved: 26 December 2022 / Online: 26 December 2022 (13:54:29 CET)
Version 8 : Received: 12 January 2023 / Approved: 12 January 2023 / Online: 12 January 2023 (02:41:45 CET)

How to cite: Botelho, F. A Duality Principle and a Concerning Convex Dual Formulation Suitable for Non-convex Variational Optimization. Preprints 2022, 2022100116. https://doi.org/10.20944/preprints202210.0116.v7 Botelho, F. A Duality Principle and a Concerning Convex Dual Formulation Suitable for Non-convex Variational Optimization. Preprints 2022, 2022100116. https://doi.org/10.20944/preprints202210.0116.v7

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MDPI and ACS Style

Botelho, F. A Duality Principle and a Concerning Convex Dual Formulation Suitable for Non-convex Variational Optimization. Preprints 2022, 2022100116. https://doi.org/10.20944/preprints202210.0116.v7

APA Style

Botelho, F. (2022). A Duality Principle and a Concerning Convex Dual Formulation Suitable for Non-convex Variational Optimization. Preprints. https://doi.org/10.20944/preprints202210.0116.v7

Chicago/Turabian Style

Botelho, F. 2022 "A Duality Principle and a Concerning Convex Dual Formulation Suitable for Non-convex Variational Optimization" Preprints. https://doi.org/10.20944/preprints202210.0116.v7

Abstract

This article develops a duality principle and a related convex dual formulation suitable 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 model in non-linear elasticity.

Keywords

Convex dual variational formulation; duality principle for non-convex optimization; model in non-linear elasticity

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: 26 December 2022
Commenter: Fabio Botelho
Commenter's Conflict of Interests: Author

Comment: Dear Sir Editor

We have replaced the section 3 of the previous article version by a much better result.

In this new version we propose a new primal-dual variational formulation for a closely related model of plates.

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