{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T03:12:37Z","timestamp":1772939557748,"version":"3.50.1"},"reference-count":35,"publisher":"Institute for Operations Research and the Management Sciences (INFORMS)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics of OR"],"published-print":{"date-parts":[[2026,1]]},"abstract":"<jats:p>We investigate a class of composite nonconvex functions, where the outer function is the sum of univariate extended-real-valued convex functions and the inner function is the limit of difference-of-convex functions. A notable feature of this class is that the inner function may fail to be locally Lipschitz continuous. It covers a range of important, yet challenging, applications, including inverse optimal value optimization and problems under value-at-risk constraints. We propose an asymptotic decomposition of the composite function that guarantees epi-convergence to the original function, leading to necessary optimality conditions for the corresponding minimization problem. The proposed decomposition also enables us to design a numerical algorithm such that any accumulation point of the generated sequence, if it exists, satisfies the newly introduced optimality conditions. These results expand on the study of so-called amenable functions introduced by Poliquin and Rockafellar in 1992, which are compositions of convex functions with smooth maps, and the prox-linear methods for their minimization. To demonstrate that our algorithmic framework is practically implementable, we further present verifiable termination criteria and preliminary numerical results.<\/jats:p>\n                  <jats:p>Funding: Financial support from the National Science Foundation Division of Computing and Communication Foundations [Grant CCF-2416172] and Division of Mathematical Sciences [Grant DMS-2416250] and the National Cancer Institute, National Institutes of Health [Grant 1R01CA287413-01] is gratefully acknowledged.<\/jats:p>","DOI":"10.1287\/moor.2023.0202","type":"journal-article","created":{"date-parts":[[2025,1,16]],"date-time":"2025-01-16T12:22:56Z","timestamp":1737030176000},"page":"1-34","source":"Crossref","is-referenced-by-count":0,"title":["Variational Theory and Algorithms for a Class of Asymptotically Approachable Nonconvex Problems"],"prefix":"10.1287","volume":"51","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-9319-6736","authenticated-orcid":false,"given":"Hanyang","family":"Li","sequence":"first","affiliation":[{"name":"Department of Industrial Engineering and Operations Research, University of California, Berkeley, California 94720"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4173-5647","authenticated-orcid":false,"given":"Ying","family":"Cui","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering and Operations Research, University of California, Berkeley, California 94720"}]}],"member":"109","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4266(02)00281-9"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-004-0515-x"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1137\/100818327"},{"key":"B4","doi-asserted-by":"publisher","DOI":"10.1007\/BF01584377"},{"key":"B5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01585997"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1137\/120889812"},{"key":"B7","doi-asserted-by":"publisher","DOI":"10.1007\/s11228-016-0362-y"},{"key":"B8","doi-asserted-by":"publisher","DOI":"10.1007\/s11228-013-0235-6"},{"key":"B9","doi-asserted-by":"publisher","DOI":"10.1137\/030601296"},{"key":"B10","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-012-0569-0"},{"key":"B11","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1975-0367131-6"},{"key":"B12","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971309"},{"key":"B13","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611976748"},{"key":"B14","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-018-1311-3"},{"key":"B15","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012992238369"},{"key":"B16","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0120959"},{"key":"B17","volume-title":"Real Analysis: Modern Techniques and Their Applications","volume":"40","author":"Folland GB","year":"1999"},{"key":"B18","doi-asserted-by":"publisher","DOI":"10.1007\/BF01584320"},{"key":"B19","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-015-0943-9"},{"key":"B20","doi-asserted-by":"publisher","DOI":"10.1137\/22M1488533"},{"key":"B21","doi-asserted-by":"publisher","DOI":"10.1137\/19M1276819"},{"key":"B22","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1994.1144"},{"key":"B23","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-019-03373-1"},{"issue":"3","key":"B24","first-page":"1","volume":"6","author":"Paleologo G","year":"2001","journal-title":"AIRO News"},{"key":"B25","volume-title":"Nonsmooth Optimization: Methods and Applications","author":"Poliquin R","year":"1992"},{"key":"B26","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1993-050-7"},{"key":"B27","doi-asserted-by":"publisher","DOI":"10.1515\/9781400873173"},{"key":"B28","doi-asserted-by":"publisher","DOI":"10.1137\/1035044"},{"key":"B29","doi-asserted-by":"publisher","DOI":"10.21314\/JOR.2000.038"},{"key":"B30","volume-title":"Variational Analysis","volume":"317","author":"Rockafellar RT","year":"2009"},{"key":"B31","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-019-01413-z"},{"key":"B32","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-022-01909-1"},{"key":"B33","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611976595"},{"key":"B34","doi-asserted-by":"publisher","DOI":"10.1007\/s11228-020-00552-2"},{"key":"B35","first-page":"31239","volume":"35","author":"Yao Y","year":"2022","journal-title":"Adv. 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