{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:21:43Z","timestamp":1760145703593,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,8,23]],"date-time":"2024-08-23T00:00:00Z","timestamp":1724371200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"TAIF University, TAIF, Saudi Arabia","award":["TU-DSPP-2024-258"],"award-info":[{"award-number":["TU-DSPP-2024-258"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we introduce and study a new class of minimization models driven by multiple integrals as cost functionals. Concretely, we formulate and establish some sufficient efficiency criteria for a feasible point in the considered optimization problem. To this end, we introduce and define the concepts of (\u0393,\u03c8)-invexity and generalized (\u0393,\u03c8)-invexity for the involved real-valued controlled multiple integral-type functionals. More precisely, we extend the notion of (generalized) (\u0393,\u03c8)-invexity to the multiple objective control models driven by multiple integral functionals. In addition, innovative proofs are considered for the principal results derived in the paper.<\/jats:p>","DOI":"10.3390\/axioms13090572","type":"journal-article","created":{"date-parts":[[2024,8,23]],"date-time":"2024-08-23T12:58:07Z","timestamp":1724417887000},"page":"572","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Sufficient Efficiency Criteria for New Classes of Non-Convex Optimization Models"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8209-3869","authenticated-orcid":false,"given":"Savin","family":"Trean\u0163\u0103","sequence":"first","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-Research Center, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7530-6264","authenticated-orcid":false,"given":"Omar Mutab","family":"Alsalami","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, College of Engineering, Taif University, Taif 21944, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1017\/S000497270000277X","article-title":"Generalized convexity and duality in multiple objective programming","volume":"39","author":"Weir","year":"1987","journal-title":"Bull. 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