Partial Derivatives and Optimization Problem on Time Scales

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Optimization Problem on Time Scales</title> <meta name="description" content="Partial Derivatives and Optimization Problem on Time Scales"> <meta name="keywords" content="Lagrange multipliers, mathematical programming, optimization problem, time scales."> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <meta name="citation_title" content="Partial Derivatives and Optimization Problem on Time Scales"> <meta name="citation_author" content="Francisco Miranda"> <meta name="citation_publication_date" content="2013/06/23"> <meta name="citation_journal_title" content="International Journal of Mathematical and Computational Sciences"> <meta name="citation_volume" content="7"> <meta name="citation_issue" content="6"> <meta name="citation_firstpage" content="1043"> <meta name="citation_lastpage" content="1048"> <meta name="citation_pdf_url" content="https://publications.waset.org/3965/pdf"> <link 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Time scale is a model of time. The language of time scales seems to be an ideal tool to unify the continuous-time and the discrete-time theories. In this work we present necessary conditions for a solution of an optimization problem on time scales. To obtain that result we use properties and results of the partial diamond-alpha derivatives for continuous-multivariable functions. These results are also presented here. <iframe src="https://publications.waset.org/3965.pdf" style="width:100%; height:400px;" frameborder="0"></iframe> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Lagrange%20multipliers" title="Lagrange multipliers">Lagrange multipliers</a>, <a href="https://publications.waset.org/search?q=mathematical%20programming" title=" mathematical programming"> mathematical programming</a>, <a href="https://publications.waset.org/search?q=optimization%20problem" title=" optimization problem"> optimization problem</a>, <a href="https://publications.waset.org/search?q=time%20scales." title=" time scales."> time scales.</a> </p> <p class="card-text"><strong>Digital Object Identifier (DOI):</strong> <a href="https://doi.org/10.5281/zenodo.1331285" target="_blank">doi.org/10.5281/zenodo.1331285</a> </p> <a href="https://publications.waset.org/3965/partial-derivatives-and-optimization-problem-on-time-scales" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/3965/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/3965/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/3965/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/3965/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/3965/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/3965/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/3965/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/3965/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/3965/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/3965/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/3965.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1725</span> </span> <p class="card-text"><strong>References:</strong></p> <br>[1] B. Aulbach and S. Hilger, "A unified approach to continuous and discrete dynamics," in Qualitative theory of differential equations (Szeged, 1988), vol. 53 of Colloq. Math. Soc. J'anos Bolyai, North-Holland, Amsterdam, 1990, pp. 37-56. <br>[2] S. Hilger, "Ein maßkettenkalk┬¿ul mit anwendung auf zentrumsmannigfaltigkeiten," Ph.D. dissertation, Universit┬¿at W┬¿urzburg, Germany, 1988. <br>[3] B. Jackson, "Partial dynamic equations on time scales," J. Comput. Appl. Math., vol. 186, no. 2, pp. 391-415, 2006. <br>[4] M. Bohner and G. SH. Guseinov, "Partial differentiation on time scales," Dynam. Systems Appl., vol. 13, pp. 351-379, 2004. <br>[5] M. Z. Sarikaya, N. Aktan, H. Yildirim, and K. İIlarslan, "Partial Δ- differentiation for multivariable functions on n-dimensional time scales," J. Math. Inequal., vol. 3, no. 2, pp. 277-291, 2009. <br>[6] P. Stehl'─▒k, "Maximum principles for elliptic dynamic equations," Math. Comput. Model., vol. 51, no. 9-10, pp. 1193-1201, 2010. <br>[7] U. M. O┬¿ zkan and B. Kaymakalan, "Basics of diamond-╬▒ partial dynamic calculus on time scales," Math. Comput. Model., vol. 50, no. 9-10, pp. 1253-1261, 2009. <br>[8] A. B. Malinowska and D. F. M. Torres, "Strong minimizers of the calculus of variations on time scales and the Weierstrass condition," in Proc. Estonian Acad. Sci. Phys. Math., vol. 58, no. 4, 2009, pp. 205-212. <br>[9] A. B. Malinowska and D. F. M. Torres, "The delta-nabla calculus of variations," Fasc. Math., vol. 44, pp. 75-83, 2010. <br>[10] A. B. Malinowska and D. F. M. Torres, "Leitmann-s direct method of optimization for absolute extrema of certain problems of the calculus of variations on time scales," Appl. Math. Comput., vol. 217, no. 3, pp. 1158-1162, 2010. <br>[11] M. Bohner, "Calculus of variations on time scales," Dynam. Systems Appl., vol. 13, no. 3-4, pp. 339-349, 2004. <br>[12] N. Martins and D. F. M. Torres, "Calculus of variations on time scales with nabla derivatives," Nonlinear Anal., vol. 71, no. 12, pp. e763-e773, 2009. <br>[13] R. A. C. Ferreira, A. B. Malinowska, and D. F. M. Torres, "Optimality conditions for the calculus of variations with higher-order delta derivatives," Appl. Math. Lett., vol. 24, no. 1, pp. 87-92, 2011. <br>[14] R. Hilscher, "Optimality conditions for time scale variational problems," D.Sc. dissertation, Masaryk University, Brno, Duben, 2008. <br>[15] M. Adivar and S.-C. Fang, "Convex optimization on mixed domains," J. Ind. Manag. Optim., vol. 8, no. 1, pp. 189-227, 2012. <br>[16] M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications. Boston, MA: Birkh┬¿auser Boston, Inc., 2001. <br>[17] M. Bohner and A. Peterson (Eds.), Advances in Dynamic Equations on Time Scales. Boston, MA: Birkh┬¿auser Boston, Inc., 2003. <br>[18] J. W. Rogers Jr. and Q. Sheng, "Notes on the diamond-╬▒ dynamic derivative on time scales," J. Math. Anal., vol. 326, no. 1, pp. 228-241, 2007. <br>[19] R. K. Sundaram, A First Course in Optimization Theory. Cambridge, UK: Cambridge University Press, 1996. <br>[20] A. B. Malinowska and D. F. M. Torres, "The diamond-alpha Riemann integral and mean value theorems on time scales," Dynam. Systems Appl., vol. 18, pp. 469-482, 2009. </div> </div> </div> </main> <footer> <div id="infolinks" class="pt-3 pb-2"> <div class="container"> <div style="background-color:#f5f5f5;" class="p-3"> <div class="row"> <div class="col-md-2"> <ul class="list-unstyled"> About <li><a href="https://waset.org/page/support">About Us</a></li> <li><a href="https://waset.org/page/support#legal-information">Legal</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/WASET-16th-foundational-anniversary.pdf">WASET celebrates its 16th foundational anniversary</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Account <li><a href="https://waset.org/profile">My Account</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Explore <li><a href="https://waset.org/disciplines">Disciplines</a></li> <li><a href="https://waset.org/conferences">Conferences</a></li> <li><a href="https://waset.org/conference-programs">Conference Program</a></li> <li><a href="https://waset.org/committees">Committees</a></li> <li><a href="https://publications.waset.org">Publications</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Research <li><a href="https://publications.waset.org/abstracts">Abstracts</a></li> <li><a href="https://publications.waset.org">Periodicals</a></li> <li><a href="https://publications.waset.org/archive">Archive</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Open Science <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Science-Philosophy.pdf">Open Science Philosophy</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Science-Award.pdf">Open Science Award</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Society-Open-Science-and-Open-Innovation.pdf">Open Innovation</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Postdoctoral-Fellowship-Award.pdf">Postdoctoral Fellowship Award</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Scholarly-Research-Review.pdf">Scholarly Research Review</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Support <li><a href="https://waset.org/page/support">Support</a></li> <li><a href="https://waset.org/profile/messages/create">Contact Us</a></li> <li><a href="https://waset.org/profile/messages/create">Report Abuse</a></li> </ul> </div> </div> </div> </div> </div> <div class="container text-center"> <hr style="margin-top:0;margin-bottom:.3rem;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" class="text-muted small">Creative Commons Attribution 4.0 International License</a> <div id="copy" class="mt-2">© 2024 World Academy of Science, Engineering and Technology</div> </div> </footer> <a href="javascript:" id="return-to-top"><i class="fas fa-arrow-up"></i></a> <div class="modal" id="modal-template"> <div class="modal-dialog"> <div class="modal-content"> <div class="row m-0 mt-1"> <div class="col-md-12"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> </div> </div> <div class="modal-body"></div> </div> </div> </div> <script src="https://cdn.waset.org/static/plugins/jquery-3.3.1.min.js"></script> <script src="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.waset.org/static/js/site.js?v=150220211556"></script> <script> jQuery(document).ready(function() { /*jQuery.get("https://publications.waset.org/xhr/user-menu", function (response) { jQuery('#mainNavMenu').append(response); });*/ jQuery.get({ url: "https://publications.waset.org/xhr/user-menu", cache: false }).then(function(response){ jQuery('#mainNavMenu').append(response); }); }); </script> </body> </html>

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Partial Derivatives and Optimization Problem on Time Scales