{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T09:10:24Z","timestamp":1778231424169,"version":"3.51.4"},"reference-count":45,"publisher":"Institute for Operations Research and the Management Sciences (INFORMS)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics of OR"],"published-print":{"date-parts":[[2026,5]]},"abstract":"<jats:p>In this paper, we introduce a homogeneous second-order descent method (HSODM) motivated from the homogenization trick in quadratic programming. The merit of homogenization is that only the leftmost eigenvector of a gradient-Hessian integrated matrix is computed at each iteration. Therefore, the algorithm is a single-loop method that does not need to switch to other sophisticated algorithms and is easy to implement. We show that HSODM has a global convergence rate of [Formula: see text] to find an [Formula: see text]-approximate second-order stationary point, and has a local quadratic convergence rate under the standard assumptions. The numerical results demonstrate the advantage of the proposed method over other second-order methods.<\/jats:p>\n                  <jats:p>Funding: This research was partially supported by the National Natural Science Foundation of China [Grants 72394360, 72394364, 72394365, 72225009, and 72171141] and by the Program for Innovative Research Team of the Shanghai University of Finance and Economics.<\/jats:p>\n                  <jats:p>Supplemental Material: Supplemental material is available at https:\/\/doi.org\/10.1287\/moor.2023.0132 .<\/jats:p>","DOI":"10.1287\/moor.2023.0132","type":"journal-article","created":{"date-parts":[[2025,5,19]],"date-time":"2025-05-19T11:31:36Z","timestamp":1747654296000},"page":"1253-1283","source":"Crossref","is-referenced-by-count":0,"title":["A Homogeneous Second-Order Descent Method for Nonconvex Optimization"],"prefix":"10.1287","volume":"51","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7135-8101","authenticated-orcid":false,"given":"Chuwen","family":"Zhang","sequence":"first","affiliation":[{"name":"Research Institute for Interdisciplinary Sciences, School of Information Management and Engineering, Shanghai University of Finance and Economics, Shanghai 200433, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-6746-3606","authenticated-orcid":false,"given":"Chang","family":"He","sequence":"additional","affiliation":[{"name":"Research Institute for Interdisciplinary Sciences, School of Information Management and Engineering, Shanghai University of Finance and Economics, Shanghai 200433, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-9323-5519","authenticated-orcid":false,"given":"Yuntian","family":"Jiang","sequence":"additional","affiliation":[{"name":"Research Institute for Interdisciplinary Sciences, School of Information Management and Engineering, Shanghai University of Finance and Economics, Shanghai 200433, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-6695-8147","authenticated-orcid":false,"given":"Chenyu","family":"Xue","sequence":"additional","affiliation":[{"name":"Research Institute for Interdisciplinary Sciences, School of Information Management and Engineering, Shanghai University of Finance and Economics, Shanghai 200433, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8924-3185","authenticated-orcid":false,"given":"Bo","family":"Jiang","sequence":"additional","affiliation":[{"name":"Research Institute for Interdisciplinary Sciences, School of Information Management and Engineering, Shanghai University of Finance and Economics, Shanghai 200433, China; and Key Laboratory of Interdisciplinary Research of Computation and Economics, Shanghai University of Finance and Economics, Ministry of Education, Shanghai 200433, China; and Dishui Lake Advanced Finance Institute, Shanghai University of Finance and Economics, Shanghai 200120, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-9328-527X","authenticated-orcid":false,"given":"Dongdong","family":"Ge","sequence":"additional","affiliation":[{"name":"Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200030, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-3239-2622","authenticated-orcid":false,"given":"Yinyu","family":"Ye","sequence":"additional","affiliation":[{"name":"Institute of Computational and Mathematical Engineering, Stanford University, Palo Alto, California 94305"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"109","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1137\/16M1058200"},{"key":"B2","doi-asserted-by":"crossref","unstructured":"Agarwal N, Allen-Zhu Z, Bullins B, Hazan E, Ma T (2017) Finding approximate local minima faster than gradient descent. 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