{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,13]],"date-time":"2023-09-13T10:26:25Z","timestamp":1694600785282},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2013,12,3]],"date-time":"2013-12-03T00:00:00Z","timestamp":1386028800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2014,6]]},"DOI":"10.1007\/s10589-013-9624-x","type":"journal-article","created":{"date-parts":[[2013,12,2]],"date-time":"2013-12-02T21:12:34Z","timestamp":1386018754000},"page":"423-454","source":"Crossref","is-referenced-by-count":7,"title":["The space decomposition theory for a class of eigenvalue optimizations"],"prefix":"10.1007","volume":"58","author":[{"given":"Ming","family":"Huang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li-Ping","family":"Pang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zun-Quan","family":"Xia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,12,3]]},"reference":[{"key":"9624_CR1","doi-asserted-by":"crossref","first-page":"527","DOI":"10.3166\/ejc.10.527-538","volume":"10","author":"P. Apkarian","year":"2004","unstructured":"Apkarian, P., Noll, D., Thevenet, J.-B., Tuan, H.D.: A spectral quadratic-SDP method with applications to fixed-order H 2 and H \u221e synthesis. Eur. J. Control 10, 527\u2013538 (2004)","journal-title":"Eur. J. Control"},{"key":"9624_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1394-9","volume-title":"Perturbation Analysis of Optimization Problems","author":"J.F. Bonnans","year":"2000","unstructured":"Bonnans, J.F., Shapiro, A.: Perturbation Analysis of Optimization Problems. Springer, New York (2000)"},{"key":"9624_CR3","volume-title":"Nonsmooth Analysis and Control Theory","author":"F.H. Clarke","year":"1998","unstructured":"Clarke, F.H., Ledyaev, Y.S., Stern, R.J., Wolenski, P.R.: Nonsmooth Analysis and Control Theory. Springer, New York (1998)"},{"key":"9624_CR4","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1007\/BF02316974","volume":"136","author":"S. Cox","year":"1996","unstructured":"Cox, S., Lipton, R.: Extremal eigenvalue problems for two-phase conductors. Arch. Ration. Mech. Anal. 136, 101\u2013117 (1996)","journal-title":"Arch. Ration. Mech. Anal."},{"key":"9624_CR5","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1007\/s10208-009-9045-5","volume":"9","author":"E.J. Cand\u00e8s","year":"2009","unstructured":"Cand\u00e8s, E.J., Recht, B.: Exact matrix completion via convex optimization. Found. Comput. Math. 9, 717\u2013772 (2009)","journal-title":"Found. Comput. Math."},{"issue":"5","key":"9624_CR6","doi-asserted-by":"crossref","first-page":"2053","DOI":"10.1109\/TIT.2010.2044061","volume":"56","author":"E.J. Cand\u00e8s","year":"2010","unstructured":"Cand\u00e8s, E.J., Tao, T.: The power of convex relaxation: near-optimal matrix completion. IEEE Trans. Inf. Theory 56(5), 2053\u20132080 (2010)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"7","key":"9624_CR7","doi-asserted-by":"crossref","first-page":"1487","DOI":"10.1002\/nme.1620350707","volume":"35","author":"A.R. Diaaz","year":"2005","unstructured":"Diaaz, A.R., Kikuchi, N.: Solution to shape and topology eigenvalue optimization problems using a homogenization method. J. Numer. Methods Eng. 35(7), 1487\u20131502 (2005)","journal-title":"J. Numer. Methods Eng."},{"key":"9624_CR8","volume-title":"Constructive Nonsmooth Analysis, Approximation & Optimization","author":"V.F. Demyanov","year":"1995","unstructured":"Demyanov, V.F., Rubinov, A.M.: Constructive Nonsmooth Analysis, Approximation & Optimization No.\u00a07. Peter Lang, Frankfurt (1995)"},{"issue":"2","key":"9624_CR9","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1137\/S1052623494274313","volume":"8","author":"T.P. Dinh","year":"1998","unstructured":"Dinh, T.P., Le Thi, H.A.: A DC optimization algorithm for solving the trust region subproblem. SIAM J. Optim. 8(2), 476\u2013505 (1998)","journal-title":"SIAM J. Optim."},{"key":"9624_CR10","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/s10479-004-5022-1","volume":"133","author":"T.P. Dinh","year":"2005","unstructured":"Dinh, T.P., Le Thi, H.A.: The DC programming and DCA revisited with DC models of real world nonconvex optimization problems. Ann. Oper. Res. 133, 23\u201346 (2005)","journal-title":"Ann. Oper. Res."},{"issue":"3","key":"9624_CR11","doi-asserted-by":"crossref","first-page":"1548","DOI":"10.1109\/TIT.2011.2104999","volume":"57","author":"D. Gross","year":"2011","unstructured":"Gross, D.: Recovering low-rank matrices from few coefficients in any basis. IEEE Trans. Inf. Theory 57(3), 1548\u20131566 (2011)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9624_CR12","volume":"105","author":"D. Gross","year":"2010","unstructured":"Gross, D., Liu, Y.-K., Flammia, S.T., Becker, S., Eisert, J.: Quantum state tomography via compressed sensing. Phys. Rev. Lett. 105, 150401 (2010)","journal-title":"Phys. Rev. Lett."},{"key":"9624_CR13","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1023\/A:1009898604624","volume":"4","author":"C. Helmberg","year":"2000","unstructured":"Helmberg, C., Rendl, F., Weismantel, R.: A semidefinite programming approach to the quadratic knapsack problem. J. Comb. Optim. 4, 197\u2013215 (2000)","journal-title":"J. Comb. Optim."},{"key":"9624_CR14","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-02796-7","volume-title":"Convex Analysis and Minimization Algorithms","author":"J.-B. Hiriart-Urruty","year":"1993","unstructured":"Hiriart-Urruty, J.-B., Lemar\u00e9chal, C.: Convex Analysis and Minimization Algorithms. Springer, Berlin (1993)"},{"key":"9624_CR15","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/s002110050109","volume":"70","author":"J.-B. Hiriart-Urruty","year":"1995","unstructured":"Hiriart-Urruty, J.-B., Ye, D.: Sensitivity analysis of all eigenvalues of a symmetric matrix. Numer. Math. 70, 45\u201372 (1995)","journal-title":"Numer. Math."},{"issue":"2","key":"9624_CR16","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/s10483-010-0214-6","volume":"31","author":"Y. Lu","year":"2010","unstructured":"Lu, Y., Pang, L.P., Xia, Z.Q.: A $\\mathcal{VU}$ -decomposition method for a second-order cone programming problem. Appl. Math. Mech. 31(2), 263\u2013270 (2010)","journal-title":"Appl. Math. Mech."},{"issue":"1","key":"9624_CR17","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1016\/j.cam.2009.12.018","volume":"234","author":"Y. Lu","year":"2010","unstructured":"Lu, Y., Pang, L.P., Guo, F.F., Xia, Z.Q.: A superlinear space decomposition algorithm for constrained nonsmooth convex program. J. Comput. Appl. Math. 234(1), 224\u2013232 (2010)","journal-title":"J. Comput. Appl. Math."},{"issue":"2","key":"9624_CR18","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1090\/S0002-9947-99-02243-6","volume":"352","author":"C. Lemar\u00e9chal","year":"2000","unstructured":"Lemar\u00e9chal, C., Oustry, F., Sagastiz\u00e1bal, C.: The ${\\mathcal{U}}$ -Lagrangian of a convex function. Trans. Am. Math. Soc. 352(2), 711\u2013729 (2000)","journal-title":"Trans. Am. Math. Soc."},{"issue":"2","key":"9624_CR19","first-page":"255","volume":"3","author":"C. Lemar\u00e9chal","year":"1996","unstructured":"Lemar\u00e9chal, C., Sagastiz\u00e1bal, C.: More than first-order developments of convex function: primal-dual relations. J. Convex Anal. 3(2), 255\u2013268 (1996)","journal-title":"J. Convex Anal."},{"key":"9624_CR20","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1017\/S0962492900002646","volume":"5","author":"A.S. Lewis","year":"1996","unstructured":"Lewis, A.S., Overton, M.L.: Eigenvalue optimization. Acta Numer. 5, 149\u2013190 (1996)","journal-title":"Acta Numer."},{"key":"9624_CR21","first-page":"2953","volume-title":"Proceedings of the American Control Conference","author":"K. Mohan","year":"2010","unstructured":"Mohan, K., Fazel, M.: Reweighted nuclear norm minimization with application to system identification. In: Proceedings of the American Control Conference, pp.\u00a02953\u20132959. IEEE Press, Piscataway (2010)"},{"issue":"2","key":"9624_CR22","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1137\/S1052623499350967","volume":"11","author":"R. Mifflin","year":"2000","unstructured":"Mifflin, R., Sagastiz\u00e1bal, C.: On $\\mathcal{VU}$ -theory for functions with primal-dual gradient structure. SIAM J. Optim. 11(2), 547\u2013571 (2000)","journal-title":"SIAM J. Optim."},{"issue":"5","key":"9624_CR23","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1080\/10556780410001704902","volume":"19","author":"R. Mifflin","year":"2004","unstructured":"Mifflin, R., Sagastiz\u00e1bal, C.: $\\mathcal{VU}$ -smoothness and proximal point results for some nonconvex functions. Optim. Methods Softw. 19(5), 463\u2013478 (2004)","journal-title":"Optim. Methods Softw."},{"key":"9624_CR24","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1007\/s10107-005-0630-3","volume":"104","author":"R. Mifflin","year":"2005","unstructured":"Mifflin, R., Sagastiz\u00e1bal, C.: A $\\mathcal{VU}$ -algorithm for convex minimization. Math. Program., Ser. B 104, 583\u2013608 (2005)","journal-title":"Math. Program., Ser. B"},{"key":"9624_CR25","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1007\/s10107-005-0634-z","volume":"104","author":"D. Noll","year":"2005","unstructured":"Noll, D., Apkarian, P.: Spectral bundle method for non-convex maximum eigenvalue functions: first-order methods. Math. Program., Ser. B 104, 701\u2013727 (2005)","journal-title":"Math. Program., Ser. B"},{"key":"9624_CR26","doi-asserted-by":"crossref","first-page":"729","DOI":"10.1007\/s10107-005-0635-y","volume":"104","author":"D. Noll","year":"2005","unstructured":"Noll, D., Apkarian, P.: Spectral bundle method for non-convex maximum eigenvalue functions: second-order methods. Math. Program., Ser. B 104, 729\u2013747 (2005)","journal-title":"Math. Program., Ser. B"},{"issue":"4","key":"9624_CR27","doi-asserted-by":"crossref","first-page":"812","DOI":"10.1080\/10556788.2011.645543","volume":"28","author":"Y.S. Niu","year":"2013","unstructured":"Niu, Y.S., Dinh, T.P., Le Thi, H.A., Judice, J.J.: Efficient DC programming approaches for the asymmetric eigenvalue complementarity problem. Optim. Methods Softw. 28(4), 812\u2013829 (2013)","journal-title":"Optim. Methods Softw."},{"issue":"1","key":"9624_CR28","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1137\/S1052623402413963","volume":"15","author":"D. Noll","year":"2004","unstructured":"Noll, D., Torki, M., Apkarian, P.: Partially augmented Lagrangian method for matrix inequality constraints. SIAM J. Optim. 15(1), 161\u2013184 (2004)","journal-title":"SIAM J. Optim."},{"issue":"2","key":"9624_CR29","doi-asserted-by":"crossref","first-page":"526","DOI":"10.1137\/S1052623496311776","volume":"9","author":"F. Oustry","year":"1999","unstructured":"Oustry, F.: The ${\\mathcal{U}}$ -Lagrangian of the maximum eigenvalue functions. SIAM J. Optim. 9(2), 526\u2013549 (1999)","journal-title":"SIAM J. Optim."},{"key":"9624_CR30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/PL00011388","volume":"89","author":"F. Oustry","year":"2000","unstructured":"Oustry, F.: A second-order bundle method to minimize the maximum eigenvalue function. Math. Program., Ser. A 89, 1\u201333 (2000)","journal-title":"Math. Program., Ser. A"},{"issue":"1","key":"9624_CR31","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1137\/0802007","volume":"2","author":"M.L. Overton","year":"1992","unstructured":"Overton, M.L.: Large-scale optimization of eigenvalues. SIAM J. Optim. 2(1), 88\u2013120 (1992)","journal-title":"SIAM J. Optim."},{"key":"9624_CR32","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/BF01585173","volume":"62","author":"M.L. Overton","year":"1993","unstructured":"Overton, M.L., Womersley, R.S.: Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices. Math. Program. 62, 321\u2013357 (1993)","journal-title":"Math. Program."},{"issue":"3","key":"9624_CR33","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1137\/S089547989324598X","volume":"16","author":"M.L. Overton","year":"1995","unstructured":"Overton, M.L., Womersley, R.S.: Second derivatives for optimizing eigenvalues of symmetric matrices. SIAM J. Matrix Anal. Appl. 16(3), 697\u2013718 (1995)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9624_CR34","first-page":"3413","volume":"12","author":"B. Recht","year":"2011","unstructured":"Recht, B.: A simpler approach to matrix completion. J. Mach. Learn. Res. 12, 3413\u20133430 (2011)","journal-title":"J. Mach. Learn. Res."},{"key":"9624_CR35","doi-asserted-by":"crossref","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"R.T. Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton University Press, New Jersey (1970)"},{"key":"9624_CR36","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-02431-3","volume-title":"Variational Analysis","author":"R.T. Rockafellar","year":"1998","unstructured":"Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Springer, Berlin (1998)"},{"issue":"3","key":"9624_CR37","doi-asserted-by":"crossref","first-page":"552","DOI":"10.1137\/0805028","volume":"5","author":"A. Shapiro","year":"1995","unstructured":"Shapiro, A., Fan, M.K.H.: On eigenvalue optimization. SIAM J. Optim. 5(3), 552\u2013556 (1995)","journal-title":"SIAM J. Optim."},{"key":"9624_CR38","first-page":"301","volume":"77","author":"A. Shapiro","year":"1997","unstructured":"Shapiro, A.: First and second order analysis of nonlinear semidefinite programs. Math. Program., Ser. B 77, 301\u2013320 (1997)","journal-title":"Math. Program., Ser. B"},{"key":"9624_CR39","volume-title":"Proceedings of the 27-th International Conference on Machine Learning","author":"M. Thiao","year":"2010","unstructured":"Thiao, M., Dinh, T.P., Le Thi, H.A.: A DC programming approach for sparse eigenvalue problem. In: Proceedings of the 27-th International Conference on Machine Learning, Haifa, Israel (2010)"},{"issue":"1","key":"9624_CR40","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1137\/1038003","volume":"38","author":"L. Vandenberghe","year":"1996","unstructured":"Vandenberghe, L., Boyd, S.: Semidefinite programming. SIAM Rev. 38(1), 49\u201395 (1996)","journal-title":"SIAM Rev."},{"issue":"5","key":"9624_CR41","doi-asserted-by":"crossref","first-page":"2095","DOI":"10.1063\/1.1636721","volume":"120","author":"Z. Zhao","year":"2004","unstructured":"Zhao, Z., Braams, B.Z., Fukuda, M., Overton, M.L., Percus, J.K.: The reduced density matrix method for electronic structure calculations and the role of three-index representability conditions. J. Chem. Phys. 120(5), 2095\u20132104 (2004)","journal-title":"J. Chem. Phys."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-013-9624-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-013-9624-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-013-9624-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,30]],"date-time":"2019-05-30T18:37:35Z","timestamp":1559241455000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-013-9624-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,12,3]]},"references-count":41,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2014,6]]}},"alternative-id":["9624"],"URL":"https:\/\/doi.org\/10.1007\/s10589-013-9624-x","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,12,3]]}}}