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

Fabio Botelho

doi:10.20944/preprints202210.0116.v8

Preprint Article Version 8 Preserved in Portico This version is not peer-reviewed

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)

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.

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

Computer Science and Mathematics, Applied Mathematics

Comment 1

Received: 12 January 2023
Commenter: Fabio Botelho
Commenter's Conflict of Interests: Author

Comment: Dear Sir Editor

We have added a new final section with a primal dual formulation for a related model in phase transition.

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

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