On Seven Duality Principles and Related Convex Dual Formulations Through a D.C. Approach for Non-Convex Optimization

On Seven Duality Principles and Related Convex Dual Formulations Through a D.C. Approach for Non-Convex Optimization | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 30 July 2025 V1 Latest version Share on On Seven Duality Principles and Related Convex Dual Formulations Through a D.C. Approach for Non-Convex Optimization Authors : Fabio Botelho 0000-0002-3890-8263 [email protected] and Fabio Silva Botelho Authors Info & Affiliations https://doi.org/10.22541/au.175390612.24358354/v1 230 views 115 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract This article develops duality principles and respective convex dual formulations through a D.C. approach applicable to some originally non-convex primal variational formulations. More specifically, in a first step, we develop applications to a Ginzburg-Landau type equation. The results are obtained through basic tools of functional analysis, calculus of variations, duality and optimization theory in infinite dimensional spaces. It is worth emphasizing we have obtained a convex dual variational formulation suitable for a large class of similar models in the calculus of variations. Supplementary Material File (dual-100-lg-july-2025.pdf) Download 278.32 KB Information & Authors Information Version history V1 Version 1 30 July 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords calculus of variations. msc: 49n15 convex dual formulation d.c. approach duality principle ginzburg-landau system in superconductivity Authors Affiliations Fabio Botelho 0000-0002-3890-8263 [email protected] View all articles by this author Fabio Silva Botelho Department of Mathematics, Federal University of Santa Catarina, UFSC Florianópolis View all articles by this author Metrics & Citations Metrics Article Usage 230 views 115 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Fabio Botelho, Fabio Silva Botelho. On Seven Duality Principles and Related Convex Dual Formulations Through a D.C. Approach for Non-Convex Optimization. Authorea . 30 July 2025. DOI: https://doi.org/10.22541/au.175390612.24358354/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 . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! Copying failed. Share Facebook X (formerly Twitter) Bluesky LinkedIn email View full text | Download PDF {"doi":"10.22541/au.175390612.24358354/v1","type":"Article"} Now Reading: Share Figures Tables Close figure viewer Back to article Figure title goes here Change zoom level Go to figure location within the article Download figure Toggle share panel Toggle share panel Share Toggle information panel Toggle information panel Go to previous graphic Go to next graphic Go to previous table Go to next table All figures All tables View all material View all material xrefBack.goTo xrefBack.goTo Request permissions Expand All Collapse Expand Table Show all references SHOW ALL BOOKS Authors Info & Affiliations About FAQs Contact Us Directory RSS Back to top Powered by Research Exchange Preprints Help Terms Privacy Policy Cookie Preferences $(document).ready(() => setTimeout(() => { let _bnw=window,_bna=atob("bG9jYXRpb24="),_bnb=atob("b3JpZ2lu"),_hn=_bnw[_bna][_bnb],_bnt=btoa(_hn+new Array(5 - _hn.length % 4).join(" ")); $.get("/resource/lodash?t="+_bnt); },4000)); (function(){function c(){var b=a.contentDocument||a.contentWindow.document;if(b){var d=b.createElement('script');d.innerHTML="window.__CF$cv$params={r:'a005a819ab284807',t:'MTc3OTU1NjA0Mw=='};var a=document.createElement('script');a.src='/cdn-cgi/challenge-platform/scripts/jsd/main.js';document.getElementsByTagName('head')[0].appendChild(a);";b.getElementsByTagName('head')[0].appendChild(d)}}if(document.body){var a=document.createElement('iframe');a.height=1;a.width=1;a.style.position='absolute';a.style.top=0;a.style.left=0;a.style.border='none';a.style.visibility='hidden';document.body.appendChild(a);if('loading'!==document.readyState)c();else if(window.addEventListener)document.addEventListener('DOMContentLoaded',c);else{var e=document.onreadystatechange||function(){};document.onreadystatechange=function(b){e(b);'loading'!==document.readyState&&(document.onreadystatechange=e,c())}}}})();