{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T17:16:37Z","timestamp":1767633397101,"version":"3.48.0"},"reference-count":30,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T00:00:00Z","timestamp":1767571200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"\u201cResearch Grant for Faculty\u201d","award":["6031"],"award-info":[{"award-number":["6031"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The aim of this article is to study duality results for nonsmooth mathematical programs with equilibrium constraints in terms of tangential subdifferentials. We study the Wolfe-type dual problem under the convexity assumptions and a Mond\u2013Weir-type dual problem is also formulated under convexity and generalized convexity assumptions for MPEC by using tangential subdifferentials. We establish weak duality and the two dual programs by assuming tangentially convex functions and also obtain strong duality theorems by assuming generalized standard Abadie constraint qualification.<\/jats:p>","DOI":"10.3390\/a19010045","type":"journal-article","created":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T12:38:56Z","timestamp":1767616736000},"page":"45","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Duality Framework for Mathematical Programs with Tangential Subdifferentials"],"prefix":"10.3390","volume":"19","author":[{"given":"Vandana","family":"Singh","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi 221005, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shashi Kant","family":"Mishra","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1950-8907","authenticated-orcid":false,"given":"Abdelouahed","family":"Hamdi","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Arts and Sciences, Qatar University, Doha P. O. Box 2713, Qatar"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Pshenichnyi, B.N. (2020). Necessary Conditions for an Extremum, CRC Press.","DOI":"10.1201\/9781003064848"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1080\/02331938608843204","article-title":"An introduction to the theory of nonsmooth optimization","volume":"17","year":"1986","journal-title":"Optimization"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1017","DOI":"10.1007\/s11590-014-0822-y","article-title":"Optimality conditions for pseudoconvex minimization over convex sets defined by tangentially convex constraints","volume":"9","year":"2015","journal-title":"Optim. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Luo, Z.Q., Pang, J.S., and Ralph, D. (1996). 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