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When simultaneously considering <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\alpha $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b1<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-approximations for all closed convex ordering cones of a fixed inner angle\u00a0<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\gamma \\in \\left[ \\frac{\\pi }{2}, \\pi \\right] $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>\u03b3<\/mml:mi>\n                    <mml:mo>\u2208<\/mml:mo>\n                    <mml:mfenced>\n                      <mml:mfrac>\n                        <mml:mi>\u03c0<\/mml:mi>\n                        <mml:mn>2<\/mml:mn>\n                      <\/mml:mfrac>\n                      <mml:mo>,<\/mml:mo>\n                      <mml:mi>\u03c0<\/mml:mi>\n                    <\/mml:mfenced>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, an approximation guarantee between\u00a0<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\alpha $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b1<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and\u00a0<jats:inline-formula><jats:alternatives><jats:tex-math>$$2 \\alpha $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mn>2<\/mml:mn>\n                    <mml:mi>\u03b1<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is achieved, which depends continuously on\u00a0<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\gamma $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b3<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. The analysis is best-possible for any inner angle and it generalizes and unifies the known results that the set of supported solutions is a 2-approximation and that the efficient set itself is a 1-approximation. Moreover, it is shown that, for maximization problems, no approximation guarantee is achievable in general by considering larger ordering cones in the described fashion, which again generalizes a known result about the set of supported solutions.<\/jats:p>","DOI":"10.1007\/s10898-023-01276-x","type":"journal-article","created":{"date-parts":[[2023,3,6]],"date-time":"2023-03-06T03:02:53Z","timestamp":1678071773000},"page":"393-415","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Approximating biobjective minimization problems using general ordering cones"],"prefix":"10.1007","volume":"86","author":[{"given":"Arne","family":"Herzel","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stephan","family":"Helfrich","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefan","family":"Ruzika","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0897-3571","authenticated-orcid":false,"given":"Clemens","family":"Thielen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,3,6]]},"reference":[{"volume-title":"Recent Developments in Vector Optimization, Vector Optimization","year":"2012","key":"1276_CR1","unstructured":"Ansari, Q.H., Yao, J.C. 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