{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,1]],"date-time":"2025-05-01T21:21:27Z","timestamp":1746134487965,"version":"3.37.3"},"reference-count":35,"publisher":"Wiley","license":[{"start":{"date-parts":[[2022,5,17]],"date-time":"2022-05-17T00:00:00Z","timestamp":1652745600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100005388","name":"Instituto Tecnol\u00f3gico de Costa Rica","doi-asserted-by":"publisher","award":["1440042"],"award-info":[{"award-number":["1440042"]}],"id":[{"id":"10.13039\/501100005388","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2022,5,17]]},"abstract":"<jats:p>Minimizing a sum of Euclidean norms (MSEN) is a classic minimization problem widely used in several applications, including the determination of single and multifacility locations. The objective of the MSEN problem is to find a vector <jats:inline-formula>\n                     <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\">\n                        <a:mi>x<\/a:mi>\n                     <\/a:math>\n                  <\/jats:inline-formula> such that it minimizes a sum of Euclidean norms of systems of equations. In this paper, we propose a modification of the MSEN problem, which we call the problem of minimizing a sum of squared Euclidean norms with rank constraint, or simply the MSSEN-RC problem. The objective of the MSSEN-RC problem is to obtain a vector <jats:inline-formula>\n                     <c:math xmlns:c=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\">\n                        <c:mi>x<\/c:mi>\n                     <\/c:math>\n                  <\/jats:inline-formula> and rank-constrained matrices <jats:inline-formula>\n                     <e:math xmlns:e=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\">\n                        <e:msub>\n                           <e:mrow>\n                              <e:mi>A<\/e:mi>\n                           <\/e:mrow>\n                           <e:mrow>\n                              <e:mn>1<\/e:mn>\n                           <\/e:mrow>\n                        <\/e:msub>\n                        <e:mo>,<\/e:mo>\n                        <e:mo>\u22ef<\/e:mo>\n                        <e:mo>,<\/e:mo>\n                        <e:msub>\n                           <e:mrow>\n                              <e:mi>A<\/e:mi>\n                           <\/e:mrow>\n                           <e:mrow>\n                              <e:mi>p<\/e:mi>\n                           <\/e:mrow>\n                        <\/e:msub>\n                     <\/e:math>\n                  <\/jats:inline-formula> such that they minimize a sum of squared Euclidean norms of systems of equations. Additionally, we present an algorithm based on the regularized alternating least-squares (RALS) method for solving the MSSEN-RC problem. We show that given the existence of critical points of the alternating least-squares method, the limit points of the converging sequences of the RALS are the critical points of the objective function. Finally, we show numerical experiments that demonstrate the efficiency of the RALS method.<\/jats:p>","DOI":"10.1155\/2022\/4838182","type":"journal-article","created":{"date-parts":[[2022,5,18]],"date-time":"2022-05-18T05:50:29Z","timestamp":1652853029000},"page":"1-14","source":"Crossref","is-referenced-by-count":2,"title":["A Regularized Alternating Least-Squares Method for Minimizing a Sum of Squared Euclidean Norms with Rank Constraint"],"prefix":"10.1155","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2903-3116","authenticated-orcid":true,"given":"Pablo","family":"Soto-Quiros","sequence":"first","affiliation":[{"name":"Escuela de Matem\u00e1tica, Instituto Tecnol\u00f3gico de Costa Rica, Cartago 30101, Costa Rica"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1109\/tgrs.2020.3004353"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1137\/s1064827598343954"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-85450-8"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1137\/s1052623497327088"},{"key":"5","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/S0377-0427(01)00357-0","article-title":"A primal\u2013dual algorithm for minimizing a sum of Euclidean norms","volume":"138","author":"L. 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