{"publication":"Automation and Remote Control","volume":85,"citation":{"mla":"Arkhipov, Pavel. “An Algorithm for Finding the Generalized Chebyshev Center of Sets Defined via Their Support Functions.” <i>Automation and Remote Control</i>, vol. 85, no. 6, Springer Nature, 2024, pp. 522–32, doi:<a href=\"https://doi.org/10.1134/S0005117924060031\">10.1134/S0005117924060031</a>.","chicago":"Arkhipov, Pavel. “An Algorithm for Finding the Generalized Chebyshev Center of Sets Defined via Their Support Functions.” <i>Automation and Remote Control</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1134/S0005117924060031\">https://doi.org/10.1134/S0005117924060031</a>.","short":"P. Arkhipov, Automation and Remote Control 85 (2024) 522–532.","ieee":"P. Arkhipov, “An algorithm for finding the generalized Chebyshev center of sets defined via their support functions,” <i>Automation and Remote Control</i>, vol. 85, no. 6. Springer Nature, pp. 522–532, 2024.","ama":"Arkhipov P. An algorithm for finding the generalized Chebyshev center of sets defined via their support functions. <i>Automation and Remote Control</i>. 2024;85(6):522-532. doi:<a href=\"https://doi.org/10.1134/S0005117924060031\">10.1134/S0005117924060031</a>","apa":"Arkhipov, P. (2024). An algorithm for finding the generalized Chebyshev center of sets defined via their support functions. <i>Automation and Remote Control</i>. Springer Nature. <a href=\"https://doi.org/10.1134/S0005117924060031\">https://doi.org/10.1134/S0005117924060031</a>","ista":"Arkhipov P. 2024. An algorithm for finding the generalized Chebyshev center of sets defined via their support functions. Automation and Remote Control. 85(6), 522–532."},"day":"01","article_processing_charge":"No","abstract":[{"lang":"eng","text":"This paper is dedicated to an optimization problem. Let A, B ⊂ Rn be compact convex sets. Consider the minimal number t0 > 0 such that t0B covers A after a shift to a vector x0 ∈ \r\nRn. The goal is to find t0 and x0. In the special case of B being a unit ball centered at zero, x0 and t0 are known as the Chebyshev center and the Chebyshev radius of A. This paper focuses on the case in which A and B are defined with their black-box support functions. An algorithm for solving such problems efficiently is suggested. The algorithm has a superlinear convergence rate, and it can solve hundred-dimensional test problems in a reasonable time, but some additional conditions on A and B are required to guarantee the presence of convergence. Additionally, the behavior of the algorithm for a simple special case is investigated, which leads to a number of theoretical results. Perturbations of this special case are also studied."}],"month":"06","OA_type":"closed access","title":"An algorithm for finding the generalized Chebyshev center of sets defined via their support functions","_id":"18482","year":"2024","publisher":"Springer Nature","author":[{"last_name":"Arkhipov","id":"b25f2ab2-1fed-11ee-8599-fe02d211784f","first_name":"Pavel","full_name":"Arkhipov, Pavel"}],"type":"journal_article","corr_author":"1","issue":"6","article_type":"original","date_created":"2024-10-27T23:01:45Z","date_updated":"2024-10-30T09:20:58Z","status":"public","oa_version":"None","intvolume":"        85","scopus_import":"1","acknowledgement":"The author is grateful to Maxim Balashov for setting the problem, providing useful literature, important discussions and text review. Also, I thank Dmitry Tsarev and Kseniia Petukhova for meaningful talks and support.","publication_identifier":{"issn":["0005-1179"],"eissn":["1608-3032"]},"department":[{"_id":"GradSch"}],"publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"522-532","quality_controlled":"1","date_published":"2024-06-01T00:00:00Z","doi":"10.1134/S0005117924060031","language":[{"iso":"eng"}]}