On Duality Principles and Concerning Convex Dual Formulations for D.C. Variational Optimization Applied to a Non-Linear Model of Plates and Related Models

2025 · doi:10.22541/au.173800499.97073391/v1
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Abstract

This article develops duality principles applicable to originally non-convex primal variational formulations. More specifically, as a first application through a D.C. approach, we establish a convex dual variational formulation for a non-linear Kirchhoff-Love plate model. The results are obtained through basic tools of functional analysis, calculus of variations, duality and optimization theory in infinite dimensional spaces. We emphasize such a convex dual formulation obtained may be applied to a large class of similar models in the calculus of variations. Finally, in the last section, we develop analogous results for a related model in superconductivity.
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Abstract

This article develops duality principles applicable to originally non-convex primal variational formulations. More specifically, as a first application through a D.C. approach, we establish a convex dual variational formulation for a non-linear Kirchhoff-Love plate model. The results are obtained through basic tools of functional analysis, calculus of variations, duality and optimization theory in infinite dimensional spaces. We emphasize such a convex dual formulation obtained may be applied to a large class of similar models in the calculus of variations. Finally, in the last section, we develop analogous results for a related model in superconductivity. Supplementary Material File (dual-plate-january-2025-2.pdf) - Download - 232.81 KB Information & Authors Information Version history Copyright This work is licensed under a Non Exclusive No Reuse License.

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Authors Metrics & Citations Metrics Article Usage 223views 117downloads Citations Download citation Fabio Botelho, Fabio Silva Botelho. On Duality Principles and Concerning Convex Dual Formulations for D.C. Variational Optimization Applied to a Non-Linear Model of Plates and Related Models. Authorea. 27 January 2025. DOI: https://doi.org/10.22541/au.173800499.97073391/v1 DOI: https://doi.org/10.22541/au.173800499.97073391/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu.

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