{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,2]],"date-time":"2024-09-02T09:11:22Z","timestamp":1725268282103},"reference-count":10,"publisher":"EDP Sciences","issue":"4","license":[{"start":{"date-parts":[[2024,9,2]],"date-time":"2024-09-02T00:00:00Z","timestamp":1725235200000},"content-version":"vor","delay-in-days":63,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100004586","name":"FAPERJ","doi-asserted-by":"crossref","award":["E-26\/205.684\/2022"],"id":[{"id":"10.13039\/501100004586","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2024,6,26]]},"published-print":{"date-parts":[[2024,7]]},"abstract":"In work of Roman A. Polyak [R.A. Polyak, Math. Program<\/jats:italic>. 92 (2002) 197\u2013235.], the Modified Chen-Harker-Kanzow-Smale (CHKS) function was studied to relate a multiplier method and an Interior Prox method with the second order distance function. Independently, the dislocated hyperbolic penalty function (DHPF) was proposed by A.E. Xavier (1992). DHPF was rewritten and studied in [L. Mallma Ramirez, N. Maculan, A.E. Xavier and V.L. Xavier, RAIRO:RO<\/jats:italic> 57 (2023) 2941\u20132950.] and [L. Mallma Ramirez, N. Maculan, A.E. Xavier and V.L. Xavier, J. Convex Anal<\/jats:italic>. To appear (2024).]. Thus, this function was called the dislocated hyperbolic function (DHF). In this work, we note that DHF is a particular case of CHKS function. Then we will call the DHF function as the dislocation hyperbolic transformation function.<\/jats:p>","DOI":"10.1051\/ro\/2024134","type":"journal-article","created":{"date-parts":[[2024,7,1]],"date-time":"2024-07-01T19:03:31Z","timestamp":1719860611000},"page":"3521-3524","source":"Crossref","is-referenced-by-count":0,"title":["A note on the dislocation hyperbolic transformation function"],"prefix":"10.1051","volume":"58","author":[{"ORCID":"http:\/\/orcid.org\/0000-0003-3579-1167","authenticated-orcid":false,"given":"Lennin Mallma","family":"Ramirez","sequence":"first","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0002-3897-3356","authenticated-orcid":false,"given":"Nelson","family":"Maculan","sequence":"additional","affiliation":[]}],"member":"250","published-online":{"date-parts":[[2024,9,2]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"2941","DOI":"10.1051\/ro\/2023153","volume":"57","author":"Mallma Ramirez","year":"2023","journal-title":"RAIRO:RO"},{"key":"R2","unstructured":"Mallma Ramirez L., Maculan N., Xavier A.E. and Xavier V.L., Dislocation hyperbolic kernel function. J. Convex Anal. To appear (2024)."},{"key":"R3","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/s101070100293","volume":"92","author":"Polyak","year":"2002","journal-title":"Math. Program."},{"key":"R4","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1007\/s10589-006-9759-0","volume":"35","author":"Polyak","year":"2006","journal-title":"Comput. Oper. Appl."},{"key":"R5","first-page":"197","volume":"92","author":"Polyak","year":"2015","journal-title":"J. Optim. Theory Appl."},{"key":"R6","unstructured":"Xavier A. E., Penaliza\u00e7\u00e3o Hiperb\u00f3lica: Um Novo M\u00e9todo para Resolu\u00e7\u00e3o de Problemas de Otimiza\u00e7\u00e3o, M.Sc. thesis, Federal University of Rio de Janeiro\/COPPE, Rio de Janeiro, Brazil (1982)."},{"key":"R7","unstructured":"Xavier A.E., Penaliza\u00e7\u00e3o Hiperb\u00f3lica, Ph.D. thesis, Federal University of Rio de Janeiro\/COPPE, Rio de Janeiro, Brazil (1992)."},{"key":"R8","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1111\/1475-3995.t01-1-00330","volume":"8","author":"Xavier","year":"2001","journal-title":"Int. Trans. Oper. Res."},{"key":"R9","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1016\/j.patcog.2009.06.018","volume":"43","author":"Xavier","year":"2010","journal-title":"Pattern Recognit."},{"key":"R10","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1287\/mnsc.13.5.344","volume":"13","author":"Zangwill","year":"1967","journal-title":"Manag. 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