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To estimate the approximate optimal range of the objective function, we extend the classical Cutting Plane Method (CPM) to the interval setting and solve the problem from two complementary perspectives. Knowing this optimal interval provides managers with essential risk-related insights. Numerical examples are presented to demonstrate the practical necessity of CINLP models and to evaluate the performance of the proposed algorithms. Additional examples are used to illustrate sufficient conditions for the convergence of the method.<\/jats:p>","DOI":"10.1142\/s1752890925500230","type":"journal-article","created":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T03:00:39Z","timestamp":1761274839000},"source":"Crossref","is-referenced-by-count":0,"title":["Optimal Values\u2019 Approximate Range of Convex Interval NonLinear Programming Problems"],"prefix":"10.1142","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7573-1751","authenticated-orcid":false,"given":"Hassan Mishmast","family":"Nehi","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0574-0580","authenticated-orcid":false,"given":"Mehdi","family":"Allahdadi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Somayeh","family":"Amirmahmoodi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2025,11,25]]},"reference":[{"key":"S1752890925500230BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/bs.adcom.2023.11.011"},{"key":"S1752890925500230BIB002","doi-asserted-by":"publisher","DOI":"10.1108\/EC-09-2023-0624"},{"key":"S1752890925500230BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-022-09391-2"},{"key":"S1752890925500230BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s11750-009-0099-y"},{"key":"S1752890925500230BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2007.03.031"},{"key":"S1752890925500230BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2014.03.029"},{"key":"S1752890925500230BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/BF02733477"},{"key":"S1752890925500230BIB008","doi-asserted-by":"publisher","DOI":"10.3103\/S0146411612040050"},{"key":"S1752890925500230BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.ymssp.2017.11.037"},{"key":"S1752890925500230BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-019-02307-6"},{"key":"S1752890925500230BIB011","doi-asserted-by":"publisher","DOI":"10.1186\/2193-1801-3-160"},{"key":"S1752890925500230BIB012","volume-title":"Optimization: Theory and Applications","author":"Rao S. 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