{"tmp":{"short":"CC BY-NC-ND (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","image":"/images/cc_by_nc_nd.png"},"publication_status":"published","year":"2003","_id":"4551","status":"public","title":"Applications of Primal-dual Interior Methods in Structural Optimization","project":[{"_id":"f432a2ee-bceb-11ed-a251-a83585c5074d","name":"Institute for Data Science Solutions"}],"publication":"Computational Methods in Applied Mathematics","date_created":"2024-04-25T13:14:17Z","user_id":"220548","citation":{"short":"R.H.W. Hoppe, S. Petrova, Computational Methods in Applied Mathematics 3 (2003) 159–176.","alphadin":"<span style=\"font-variant:small-caps;\">Hoppe, Ronald H. W.</span> ; <span style=\"font-variant:small-caps;\">Petrova, Svetozara</span>: Applications of Primal-dual Interior Methods in Structural Optimization. In: <i>Computational Methods in Applied Mathematics</i> Bd. 3, Walter de Gruyter GmbH (2003), Nr. 1, S. 159–176","apa":"Hoppe, R. H. W., &#38; Petrova, S. (2003). Applications of Primal-dual Interior Methods in Structural Optimization. <i>Computational Methods in Applied Mathematics</i>, <i>3</i>(1), 159–176. <a href=\"https://doi.org/10.2478/cmam-2003-0011\">https://doi.org/10.2478/cmam-2003-0011</a>","chicago":"Hoppe, Ronald H. W., and Svetozara Petrova. “Applications of Primal-Dual Interior Methods in Structural Optimization.” <i>Computational Methods in Applied Mathematics</i> 3, no. 1 (2003): 159–76. <a href=\"https://doi.org/10.2478/cmam-2003-0011\">https://doi.org/10.2478/cmam-2003-0011</a>.","ieee":"R. H. W. Hoppe and S. Petrova, “Applications of Primal-dual Interior Methods in Structural Optimization,” <i>Computational Methods in Applied Mathematics</i>, vol. 3, no. 1, pp. 159–176, 2003.","bibtex":"@article{Hoppe_Petrova_2003, title={Applications of Primal-dual Interior Methods in Structural Optimization}, volume={3}, DOI={<a href=\"https://doi.org/10.2478/cmam-2003-0011\">10.2478/cmam-2003-0011</a>}, number={1}, journal={Computational Methods in Applied Mathematics}, publisher={Walter de Gruyter GmbH}, author={Hoppe, Ronald H. W. and Petrova, Svetozara}, year={2003}, pages={159–176} }","mla":"Hoppe, Ronald H. W., and Svetozara Petrova. “Applications of Primal-Dual Interior Methods in Structural Optimization.” <i>Computational Methods in Applied Mathematics</i>, vol. 3, no. 1, Walter de Gruyter GmbH, 2003, pp. 159–76, doi:<a href=\"https://doi.org/10.2478/cmam-2003-0011\">10.2478/cmam-2003-0011</a>.","ama":"Hoppe RHW, Petrova S. Applications of Primal-dual Interior Methods in Structural Optimization. <i>Computational Methods in Applied Mathematics</i>. 2003;3(1):159-176. doi:<a href=\"https://doi.org/10.2478/cmam-2003-0011\">10.2478/cmam-2003-0011</a>"},"keyword":["structural optimization","nonlinear programming","primal-dual interior-point methods","eddy current equations","elasticity equations"],"doi":"10.2478/cmam-2003-0011","volume":3,"oa":"1","publisher":"Walter de Gruyter GmbH","issue":"1","author":[{"last_name":"Hoppe","full_name":"Hoppe, Ronald H. W.","first_name":"Ronald H. W."},{"id":"201871","first_name":"Svetozara","last_name":"Petrova","full_name":"Petrova, Svetozara"}],"date_updated":"2024-04-30T08:12:12Z","page":"159-176","language":[{"iso":"eng"}],"intvolume":"         3","main_file_link":[{"open_access":"1"}],"type":"journal_article","publication_identifier":{"eissn":["1609-9389"],"issn":["1609-4840"]},"abstract":[{"text":"We are concerned with structural optimization problems for technological processes in material science that are described by partial differential equations. In particular, we consider the topology optimization of conductive media in high-power electronic devices described by Maxwell equations and the optimal design of composite ceramic materials by homogenization modeling. All these tasks lead to constrained nonconvex minimization problems with both equality and inequality constraints on the state variables and design parameters. After discretization by finite elements, we solve the discretized optimization problems by a primal-dual Newton interior-point method. Within a line-search approach, transforming iterations are applied with respect to the null space decomposition of the condensed primal-dual system to find the search direction. Some numerical experiments for the two applications are presented.\r\n                ","lang":"eng"}]}