{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T00:13:37Z","timestamp":1743034417541,"version":"3.40.3"},"publisher-location":"Cham","reference-count":22,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031598340"},{"type":"electronic","value":"9783031598357"}],"license":[{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024]]},"DOI":"10.1007\/978-3-031-59835-7_20","type":"book-chapter","created":{"date-parts":[[2024,5,21]],"date-time":"2024-05-21T07:05:03Z","timestamp":1716275103000},"page":"265-279","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On the Partial Convexification of the Low-Rank Spectral Optimization: Rank Bounds and Algorithms"],"prefix":"10.1007","author":[{"given":"Yongchun","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weijun","family":"Xie","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,5,22]]},"reference":[{"issue":"2","key":"20_CR1","doi-asserted-by":"publisher","first-page":"514","DOI":"10.1137\/21M1398677","volume":"4","author":"A Askari","year":"2022","unstructured":"Askari, A., d\u2019Aspremont, A., Ghaoui, L.E.: Approximation bounds for sparse programs. SIAM J. Math. Data Sci. 4(2), 514\u2013530 (2022)","journal-title":"SIAM J. Math. Data Sci."},{"issue":"2","key":"20_CR2","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1007\/BF02574037","volume":"13","author":"AI Barvinok","year":"1995","unstructured":"Barvinok, A.I.: Problems of distance geometry and convex properties of quadratic maps. Discret. Comput. Geom. 13(2), 189\u2013202 (1995)","journal-title":"Discret. Comput. Geom."},{"key":"20_CR3","doi-asserted-by":"crossref","unstructured":"Bedoya, J.C., Abdelhadi, A., Liu, C.C., Dubey, A.: A QCQP and SDP formulation of the optimal power flow including renewable energy resources. In: 2019 International Symposium on Systems Engineering (ISSE), pp. 1\u20138. IEEE (2019)","DOI":"10.1109\/ISSE46696.2019.8984430"},{"key":"20_CR4","doi-asserted-by":"crossref","unstructured":"Ben-Tal, A., Nemirovski, A.: Lectures on modern convex optimization: analysis, algorithms, and engineering applications. SIAM (2001)","DOI":"10.1137\/1.9780898718829"},{"key":"20_CR5","unstructured":"Bertsimas, D., Cory-Wright, R., Pauphilet, J.: A new perspective on low-rank optimization. arXiv preprint arXiv:2105.05947 (2021)"},{"issue":"2","key":"20_CR6","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1007\/s10107-002-0352-8","volume":"95","author":"S Burer","year":"2003","unstructured":"Burer, S., Monteiro, R.D.: A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization. Math. Program. 95(2), 329\u2013357 (2003)","journal-title":"Math. Program."},{"issue":"3","key":"20_CR7","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1007\/s10107-004-0564-1","volume":"103","author":"S Burer","year":"2005","unstructured":"Burer, S., Monteiro, R.D.: Local minima and convergence in low-rank semidefinite programming. Math. Program. 103(3), 427\u2013444 (2005)","journal-title":"Math. Program."},{"issue":"1","key":"20_CR8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10107-019-01367-2","volume":"181","author":"S Burer","year":"2020","unstructured":"Burer, S., Ye, Y.: Exact semidefinite formulations for a class of (random and non-random) nonconvex quadratic programs. Math. Program. 181(1), 1\u201317 (2020)","journal-title":"Math. Program."},{"key":"20_CR9","doi-asserted-by":"publisher","unstructured":"Deza, M.M., Laurent, M., Weismantel, R.: Geometry of Cuts and Metrics, vol.\u00a02. Springer, Berlin, Heidelberg (1997). https:\/\/doi.org\/10.1007\/978-3-642-04295-9","DOI":"10.1007\/978-3-642-04295-9"},{"key":"20_CR10","unstructured":"Drusvyatskiy, D., Kempton, C.: Variational analysis of spectral functions simplified. arXiv preprint arXiv:1506.05170 (2015)"},{"key":"20_CR11","doi-asserted-by":"crossref","unstructured":"Eltved, A., Burer, S.: Strengthened SDP relaxation for an extended trust region subproblem with an application to optimal power flow. Math. Program. 1\u201326 (2022)","DOI":"10.1007\/s10107-021-01737-9"},{"issue":"4","key":"20_CR12","doi-asserted-by":"publisher","first-page":"2547","DOI":"10.1287\/moor.2021.1219","volume":"47","author":"J Kim","year":"2022","unstructured":"Kim, J., Tawarmalani, M., Richard, J.P.P.: Convexification of permutation-invariant sets and an application to sparse principal component analysis. Math. Oper. Res. 47(4), 2547\u20132584 (2022)","journal-title":"Math. Oper. Res."},{"key":"20_CR13","unstructured":"Kulis, B., Sustik, M.A., Dhillon, I.S.: Low-rank kernel learning with bregman matrix divergences. J. Mach. Learn. Res. 10(2) (2009)"},{"key":"20_CR14","doi-asserted-by":"crossref","unstructured":"Lau, L.C., Ravi, R., Singh, M.: Iterative Methods in Combinatorial Optimization, vol.\u00a046. Cambridge University Press, Cambridge (2011)","DOI":"10.1017\/CBO9780511977152"},{"key":"20_CR15","unstructured":"Li, Y., Xie, W.: On the exactness of Dantzig-Wolfe relaxation for rank constrained optimization problems. arXiv preprint arXiv:2210.16191 (2022)"},{"key":"20_CR16","doi-asserted-by":"crossref","unstructured":"Li, Y., Xie, W.: On the partial convexification for low-rank spectral optimization: rank bounds and algorithms. arXiv preprint arXiv:2305.07638 (2023)","DOI":"10.1007\/978-3-031-59835-7_20"},{"issue":"2","key":"20_CR17","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1287\/moor.23.2.339","volume":"23","author":"G Pataki","year":"1998","unstructured":"Pataki, G.: On the rank of extreme matrices in semidefinite programs and the multiplicity of optimal eigenvalues. Math. Oper. Res. 23(2), 339\u2013358 (1998)","journal-title":"Math. Oper. Res."},{"key":"20_CR18","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1972)"},{"key":"20_CR19","unstructured":"Samadi, S., Tantipongpipat, U., Morgenstern, J.H., Singh, M., Vempala, S.: The price of fair PCA: one extra dimension. Adv. Neural Inf. Process. Syst. 31 (2018)"},{"key":"20_CR20","unstructured":"Tantipongpipat, U., Samadi, S., Singh, M., Morgenstern, J.H., Vempala, S.: Multi-criteria dimensionality reduction with applications to fairness. Adv. Neural Inf. Process. Syst. 32 (2019)"},{"issue":"1","key":"20_CR21","doi-asserted-by":"publisher","first-page":"304","DOI":"10.1109\/TSP.2010.2084997","volume":"59","author":"H Yu","year":"2010","unstructured":"Yu, H., Lau, V.K.: Rank-constrained schur-convex optimization with multiple trace\/log-det constraints. IEEE Trans. Signal Process. 59(1), 304\u2013314 (2010)","journal-title":"IEEE Trans. Signal Process."},{"key":"20_CR22","doi-asserted-by":"crossref","unstructured":"Zhang, D., Hu, Y., Ye, J., Li, X., He, X.: Matrix completion by truncated nuclear norm regularization. In: 2012 IEEE Conference on Computer Vision and Pattern Recognition, pp. 2192\u20132199. IEEE (2012)","DOI":"10.1109\/CVPR.2012.6247927"}],"container-title":["Lecture Notes in Computer Science","Integer Programming and Combinatorial Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-59835-7_20","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T14:32:00Z","timestamp":1732026720000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-59835-7_20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024]]},"ISBN":["9783031598340","9783031598357"],"references-count":22,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-59835-7_20","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2024]]},"assertion":[{"value":"22 May 2024","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"IPCO","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Integer Programming and Combinatorial Optimization","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Wroc\u0142aw","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Poland","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"3 July 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"5 July 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"25","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"ipco2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/ipco2024.ii.uni.wroc.pl\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}