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Each algorithm is based on a directional search method in which the search path at each iteration is either a ray or a two-dimensional circular arc in <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathbb {R}}^n$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mrow>\n                      <mml:mi>R<\/mml:mi>\n                    <\/mml:mrow>\n                    <mml:mi>n<\/mml:mi>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. At each iteration, a search path is constructed by intersecting bisectors of pairs of points, where the bisectors are either hyperplanes or <jats:italic>n<\/jats:italic>-dimensional spheres. Each search path preserves complementary slackness and primal (dual) feasibility for the primal (dual) algorithm. The step size along each search path is determined explicitly. Test problems up to 1000 dimensions and 10,000 points were solved to optimality by both primal and dual algorithms. Computational results also show that these algorithms outperform several open-source SOCP codes.<\/jats:p>","DOI":"10.1007\/s10589-024-00599-z","type":"journal-article","created":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T08:02:36Z","timestamp":1723104156000},"page":"553-574","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The weighted Euclidean one-center problem in $${\\mathbb {R}}^n$$"],"prefix":"10.1007","volume":"89","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5903-9482","authenticated-orcid":false,"given":"Mark E.","family":"Cawood","sequence":"first","affiliation":[]},{"given":"P. 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