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

Fabio Botelho

doi:10.20944/preprints202210.0116.v2

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preprints.org > computer science and mathematics > applied mathematics > doi: 10.20944/preprints202210.0116.v2

Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed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.v2 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.v2

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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.v2

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.v2

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.v2

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: 11 October 2022
Commenter: Fabio Botelho
Commenter's Conflict of Interests: Author

Comment: Dear Sir Editor

Some typos have been corrected.

Also, we have divided the problem into two cases, namely, negative definite and positive definite stress tensors, which guarantees convexity in the variable u for the primal penalized formulation. in each separate case.

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