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Optim."],"published-print":{"date-parts":[[2026,9,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this paper, we present a novel framework for addressing the completely positive tensor decomposition problem with ideal-sparsity. First, we introduce a definition of maximal cliques of multi-hypergraphs associated with completely positive tensors. Furthermore, we propose a theoretically guaranteed algorithm to generate all such maximal cliques and establish a necessary condition for tensors to be completely positive. Second, we reformulate the completely positive tensor decomposition problem into an ideal-sparse generalized moment problem. This reformulation involves optimizing over several lower-dimensional measure variables supported on the maximal cliques of a multi-hypergraph, enabling a more efficient solution process. We apply moment-based relaxations to solve this reformulation. We prove not only the asymptotic convergence but also the finite convergence of this ideal-sparse moment hierarchy. Numerical results show that the ideal-sparse reformulation is faster to compute than the original dense formulation of completely positive tensor decomposition problems.<\/jats:p>","DOI":"10.1137\/25m1770990","type":"journal-article","created":{"date-parts":[[2026,7,20]],"date-time":"2026-07-20T15:41:20Z","timestamp":1784562080000},"page":"1537-1562","source":"Crossref","is-referenced-by-count":0,"title":["An Ideal-Sparse Generalized Moment Problem Reformulation for Completely Positive Tensor Decomposition Exploiting Maximal Cliques of Multi-hypergraphs"],"prefix":"10.1137","volume":"36","author":[{"given":"Pengfei","family":"Huang","sequence":"first","affiliation":[{"name":"School of Mathematics, Hunan University, Changsha 410082, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9960-6138","authenticated-orcid":true,"given":"Minru","family":"Bai","sequence":"additional","affiliation":[{"name":"Corresponding author. School of Mathematics, Hunan University, Changsha 410082, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,7,20]]},"reference":[{"key":"ref1","doi-asserted-by":"crossref","unstructured":"A. Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, SIAM, Philadelphia, 2001.","DOI":"10.1137\/1.9780898718829"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1137\/141000671"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-020-01233-w"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1002\/9780470747278"},{"key":"ref5","volume":"119","author":"Curto R. E.","year":"1996","journal-title":"Mem. Amer. Math. 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Hazan, Non-negative tensor factorization with applications to statistics and computer vision, in ICML \u201905: Proceedings of the 22nd International Conference on Machine Learning, ACM, New York, 2005, pp. 792\u2013799, https:\/\/doi.org\/10.1145\/1102351.1102451.","DOI":"10.1145\/1102351.1102451"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1142\/S1793830917500781"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1137\/050623802"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1137\/20M1323564"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1137\/19M1307871"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1145\/3569709"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-024-00574-8"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2014.09.064"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2016.08.016"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","deposited":{"date-parts":[[2026,7,20]],"date-time":"2026-07-20T15:41:23Z","timestamp":1784562083000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/25M1770990"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,20]]},"references-count":35,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2026,9,30]]}},"alternative-id":["10.1137\/25M1770990"],"URL":"https:\/\/doi.org\/10.1137\/25m1770990","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,20]]}}}