{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:53:16Z","timestamp":1760151196882,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,2,11]],"date-time":"2022-02-11T00:00:00Z","timestamp":1644537600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/04106\/2020"],"award-info":[{"award-number":["UIDB\/04106\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this paper, we continue an earlier study of the regularization procedures of linear copositive problems and present new algorithms that can be considered as modifications of the algorithm described in our previous publication, which is based on the concept of immobile indices. The main steps of the regularization algorithms proposed in this paper are explicitly described and interpreted from the point of view of the facial geometry of the cone of copositive matrices. The results of the paper provide a deeper understanding of the structure of feasible sets of copositive problems and can be useful for developing a duality theory for these problems.<\/jats:p>","DOI":"10.3390\/a15020059","type":"journal-article","created":{"date-parts":[[2022,2,13]],"date-time":"2022-02-13T20:32:30Z","timestamp":1644784350000},"page":"59","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Regularization Algorithms for Linear Copositive Programming Problems: An Approach Based on the Concept of Immobile Indices"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0959-0831","authenticated-orcid":false,"given":"Olga","family":"Kostyukova","sequence":"first","affiliation":[{"name":"Institute of Mathematics, National Academy of Sciences of Belarus, Surganov Str. 11, 220072 Minsk, Belarus"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2678-2552","authenticated-orcid":false,"given":"Tatiana","family":"Tchemisova","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Campus Universit\u00e1rio Santiago, University of Aveiro, 3810-193 Aveiro, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1016\/j.ejor.2011.04.026","article-title":"Copositive optimization -recent developments and applications","volume":"216","author":"Bomze","year":"2012","journal-title":"EJOR"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"875","DOI":"10.1137\/S1052623401383248","article-title":"Approximation of the stability number number of a graph via copositive programming","volume":"12","author":"Pasechnik","year":"2002","journal-title":"SIAM J. Optim."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Diehl, M., Glineur, F., Jarlebring, E., and Michielis, W. (2010). Copositive Programming\u2014A survey. Recent Advances in Optimization and Its Applications in Engineering, Springer.","DOI":"10.1007\/978-3-642-12598-0"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1051\/ro\/2018034","article-title":"A guide to conic optimisation and its applications","volume":"52","author":"Letchford","year":"2018","journal-title":"RAIRO\u2013Rech. Oper. Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1007\/s10957-013-0344-2","article-title":"Copositive Programming via semi-infinite optimization","volume":"159","author":"Ahmed","year":"2013","journal-title":"J. Optim. Theory Appl."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Anjos, M.F., and Lasserre, J.B. (2012). 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