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Firstly, we introduce the concepts of <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\varepsilon $$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b5<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>-efficient elements and weakly <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\varepsilon $$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b5<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>-efficient elements of a set with VOSs given by coradiant sets. Secondly we derive characterization theorems for weakly <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\varepsilon $$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b5<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>-efficient solutions in the sense of linear scalarization. Then, we establish characterization theorems for weakly <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\varepsilon $$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b5<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>-efficient solutions in the sense of nonlinear scalarization via the Hirriart-Urruty nonlinear functions and the functions defined via the Kasimbeyli\u2019s augmented dual cones. Finally, we establish nonlinear scalarization theorems for the weakly <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\varepsilon $$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b5<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>-efficient elements of a set via the augmented dual cones approach. The results of this paper generalize the corresponding results in the literature.<\/jats:p>","DOI":"10.1007\/s10957-025-02662-z","type":"journal-article","created":{"date-parts":[[2025,5,2]],"date-time":"2025-05-02T13:37:39Z","timestamp":1746193059000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Linear and Nonlinear Scalarization Methods for Vector Optimization Problems with Variable Ordering Structures"],"prefix":"10.1007","volume":"206","author":[{"given":"Jian-Wen","family":"Peng","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wen-Bin","family":"Wei","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7339-9409","authenticated-orcid":false,"given":"Refail","family":"Kasimbeyli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,5,2]]},"reference":[{"key":"2662_CR1","doi-asserted-by":"publisher","first-page":"695","DOI":"10.1007\/s11228-021-00615-y","volume":"30","author":"TQ Bao","year":"2022","unstructured":"Bao, T.Q., Mordukhovich, B.S., Soubeyran, A., Tammer, C.: Vector optimization with domination structures: variational principles and applications. 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