{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:24:23Z","timestamp":1760145863107,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T00:00:00Z","timestamp":1726012800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we investigate and characterize a family of optimization problems introduced by interval-valued functionals that are determined by curvilinear integrals. To this end, we first state the path independence and (strictly) LU convexity properties of the considered functionals. Thereafter, we formulate the corresponding controlled variational inequalities. The main results of this paper provide some connections for the above-mentioned variational models. Since the objective functionals have a physical importance, an illustrative application is considered and studied by using the theoretical elements obtained in this study.<\/jats:p>","DOI":"10.3390\/axioms13090614","type":"journal-article","created":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T05:45:12Z","timestamp":1726033512000},"page":"614","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Connections between Some Extremization Problems and Associated Inequalities"],"prefix":"10.3390","volume":"13","author":[{"given":"Wei","family":"Xu","sequence":"first","affiliation":[{"name":"Computer Science Department, New York University, 251 Mercer Street, New York, NY 10012, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8209-3869","authenticated-orcid":false,"given":"Savin","family":"Trean\u0163\u0103","sequence":"additional","affiliation":[{"name":"Faculty of Applied Sciences, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania"},{"name":"Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania"},{"name":"Fundamental Sciences Applied in Engineering\u2014Research Center, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1007\/BF02392210","article-title":"On some non-linear elliptic differential-functional equations","volume":"115","author":"Hartman","year":"1966","journal-title":"Acta Math."},{"key":"ref_2","unstructured":"Giannessi, F. 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