{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:40:47Z","timestamp":1760161247999},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2015,3,4]],"date-time":"2015-03-04T00:00:00Z","timestamp":1425427200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2015,9]]},"DOI":"10.1007\/s10898-015-0273-8","type":"journal-article","created":{"date-parts":[[2015,3,3]],"date-time":"2015-03-03T10:30:09Z","timestamp":1425378609000},"page":"77-97","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Second-order conditions for existence of augmented Lagrange multipliers for eigenvalue composite optimization problems"],"prefix":"10.1007","volume":"63","author":[{"given":"Chao","family":"Kan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wen","family":"Song","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,3,4]]},"reference":[{"key":"273_CR1","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-9467-7","volume-title":"Convex Analysis and Monotone Operator Theory in Hilbert Spaces. CMS Books in Mathematics","author":"HH Bauschke","year":"2011","unstructured":"Bauschke, H.H., Combettes, P.L.: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. CMS Books in Mathematics. Springer, New York (2011)"},{"key":"273_CR2","volume-title":"Introduction to Matrix Analysis","author":"R Bellman","year":"1970","unstructured":"Bellman, R.: Introduction to Matrix Analysis, 2nd edn. McGraw-Hill, New York (1970)","edition":"2"},{"key":"273_CR3","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1394-9","volume-title":"Perturbation Analysis of Optimization Problems","author":"JF Bonnans","year":"2000","unstructured":"Bonnans, J.F., Shapiro, A.: Perturbation Analysis of Optimization Problems. Springer, New York (2000)"},{"key":"273_CR4","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/BFb0120698","volume":"3","author":"J Cullum","year":"1975","unstructured":"Cullum, J., Donath, W.E., Wolfe, P.: The minimization of certain nondifferentiable sums of eigenvalues of symmetric matrices. Math. Program. Study 3, 35\u201355 (1975)","journal-title":"Math. Program. Study"},{"key":"273_CR5","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1137\/10081085X","volume":"22","author":"D Fern\u00e1ndez","year":"2012","unstructured":"Fern\u00e1ndez, D., Solodov, M.V.: Local convergence of exact and inexact augmented Lagrangian methods under the second-order sufficient optimality condition. SIAM J. Optim. 22, 384\u2013407 (2012)","journal-title":"SIAM J. Optim."},{"key":"273_CR6","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1137\/0323032","volume":"23","author":"R Fletcher","year":"1985","unstructured":"Fletcher, R.: Semi-definite matrix constraints in optimization. SIAM J. Control Optim. 23, 493\u2013513 (1985)","journal-title":"SIAM J. Control Optim."},{"key":"273_CR7","volume-title":"Practical Methods of Optimization","author":"R Fletcher","year":"1987","unstructured":"Fletcher, R.: Practical Methods of Optimization, 2nd edn. Wiley, Chichester (1987)","edition":"2"},{"key":"273_CR8","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1080\/03081088108817381","volume":"9","author":"S Friedland","year":"1981","unstructured":"Friedland, S.: Convex spectral functions. Linear Multilinear Algebra 9, 299\u2013316 (1981)","journal-title":"Linear Multilinear Algebra"},{"key":"273_CR9","doi-asserted-by":"crossref","first-page":"1168","DOI":"10.1137\/050626090","volume":"4","author":"PL Combettes","year":"2005","unstructured":"Combettes, P.L., Wajs, V.R.: Signal recovery by proximal forward-backward splitting. Multiscale Model. Simul. 4, 1168\u20131200 (2005)","journal-title":"Multiscale Model. Simul."},{"key":"273_CR10","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1090\/S0002-9947-1992-1088019-1","volume":"334","author":"Chi Ngoc Do","year":"1992","unstructured":"Do, Chi Ngoc: Generalized second-order derivatives of convex function in reflexive Banach spaces. Trans. Amer. Math. Soc. 334, 281\u2013301 (1992)","journal-title":"Trans. Amer. Math. Soc."},{"key":"273_CR11","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1080\/03601218008907358","volume":"8","author":"EJ Haug","year":"1980","unstructured":"Haug, E.J., Rousselet, B.: Design sensitivity analysis in structural mechanics II: eigenvalue variation. J. Struct. Mech. 8, 161\u2013186 (1980)","journal-title":"J. Struct. Mech."},{"key":"273_CR12","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."},{"key":"273_CR13","doi-asserted-by":"crossref","first-page":"576","DOI":"10.1287\/moor.21.3.576","volume":"21","author":"AS Lewis","year":"1996","unstructured":"Lewis, A.S.: Derivatives of spectral functions. Math. Oper. Res. 21, 576\u2013588 (1996)","journal-title":"Math. Oper. Res."},{"key":"273_CR14","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1137\/S089547980036838X","volume":"23","author":"AS Lewis","year":"2001","unstructured":"Lewis, A.S., Sendov, H.S.: Twice differentiable spectral functions. SIAM. J. Matrix Anal. Appl. 23, 368\u2013386 (2001)","journal-title":"SIAM. J. Matrix Anal. Appl."},{"key":"273_CR15","doi-asserted-by":"crossref","first-page":"1359","DOI":"10.1016\/j.na.2006.07.022","volume":"67","author":"YJ Liu","year":"2007","unstructured":"Liu, Y.J., Zhang, L.W.: Convergence analysis of the augmented Lagrangian method for nonlinear second-order cone optimization problem. Nonlinear Anal. 67, 1359\u20131373 (2007)","journal-title":"Nonlinear Anal."},{"key":"273_CR16","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1137\/0609021","volume":"9","author":"ML Overton","year":"1988","unstructured":"Overton, M.L.: On minimizing the maximum eigenvalue of a symmetric matrix. SIAM J. Matrix Anal. Appl. 9, 256\u2013268 (1988)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"273_CR17","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1137\/0802007","volume":"2","author":"ML Overton","year":"1992","unstructured":"Overton, M.L.: Large-scale optimization of eigenvalues. SIAM J. Optim. 2, 88\u2013120 (1992)","journal-title":"SIAM J. Optim."},{"key":"273_CR18","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/BF01585173","volume":"62","author":"ML Overton","year":"1993","unstructured":"Overton, M.L., Womersley, R.S.: Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmtric matrix. Math. Program. Ser. B 62, 321\u2013357 (1993)","journal-title":"Math. Program. Ser. B"},{"key":"273_CR19","doi-asserted-by":"crossref","first-page":"1805","DOI":"10.1090\/S0002-9947-96-01544-9","volume":"348","author":"RA Poliquin","year":"1996","unstructured":"Poliquin, R.A., Rockafellar, R.T.: Prox-regular functions in variational analysis. Trans. Amer. Math. Soc. 348, 1805\u20131838 (1996)","journal-title":"Trans. Amer. Math. Soc."},{"key":"273_CR20","doi-asserted-by":"crossref","first-page":"1121","DOI":"10.1137\/S1052623494279316","volume":"6","author":"R Poliquin","year":"1996","unstructured":"Poliquin, R., Rockafellar, R.T.: Generalized Hessian properties of regularized nonsmooth functions. SIAM J. Optim. 6, 1121\u20131137 (1996)","journal-title":"SIAM J. Optim."},{"key":"273_CR21","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1137\/0312021","volume":"12","author":"RT Rockafellar","year":"1974","unstructured":"Rockafellar, R.T.: Augmented Lagrange multiplier functions and duality in nonconvex programming. SIAM J. Control 12, 268\u2013285 (1974)","journal-title":"SIAM J. Control"},{"key":"273_CR22","doi-asserted-by":"crossref","unstructured":"Rockafellar, R.T.: Conjugate duality and optimization, regional conference series in applied mathematics. SIAM, Philadelphia (1974)","DOI":"10.1137\/1.9781611970524"},{"key":"273_CR23","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1090\/S0002-9947-1988-0936806-9","volume":"307","author":"RT Rockafellar","year":"1988","unstructured":"Rockafellar, R.T.: First- and second-order epi-differentiability in nonlinear programming. Trans. Amer. Math. Soc. 307, 75\u2013108 (1988)","journal-title":"Trans. Amer. Math. Soc."},{"key":"273_CR24","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1090\/S0002-9947-1990-1031242-0","volume":"322","author":"RT Rockafellar","year":"1990","unstructured":"Rockafellar, R.T.: Generalized second derivatives of convex functions and saddle function. Trans. Amer. Math. Soc. 322, 51\u201377 (1990)","journal-title":"Trans. Amer. Math. Soc."},{"key":"273_CR25","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1137\/1035044","volume":"35","author":"RT Rockafellar","year":"1993","unstructured":"Rockafellar, R.T.: Lagrange multipliers and optimality. SIAM Rev. 35, 183\u2013238 (1993)","journal-title":"SIAM Rev."},{"key":"273_CR26","doi-asserted-by":"crossref","first-page":"462","DOI":"10.1287\/moor.14.3.462","volume":"14","author":"RT Rockafellar","year":"1989","unstructured":"Rockafellar, R.T.: Second-order optimality conditions in nonlinear programming obtained by way of epi-derivatives. Math. Oper. Res. 14, 462\u2013484 (1989)","journal-title":"Math. Oper. Res."},{"key":"273_CR27","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-02431-3","volume-title":"Variational Analysis","author":"RT Rockafellar","year":"1998","unstructured":"Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Springer, New York (1998)"},{"key":"273_CR28","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1287\/moor.1040.0103","volume":"29","author":"A Shapiro","year":"2004","unstructured":"Shapiro, A., Sun, J.: Some properties of the augmented Lagrangian in cone constrained optimization. Math. Oper. Res. 29, 479\u2013491 (2004)","journal-title":"Math. Oper. Res."},{"key":"273_CR29","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1007\/BF01443623","volume":"18","author":"A Shapiro","year":"1988","unstructured":"Shapiro, A.: Perturbation theory of nonlinear programs when the set of optimal solutions is not a singleton. Appl. math. Optim. 18, 215\u2013229 (1988)","journal-title":"Appl. math. Optim."},{"key":"273_CR30","doi-asserted-by":"crossref","first-page":"552","DOI":"10.1137\/0805028","volume":"3","author":"A Shapiro","year":"1995","unstructured":"Shapiro, A., Fan, M.K.H.: On eigenvalue optimization. SIAM J. Optim. 3, 552\u2013568 (1995)","journal-title":"SIAM J. Optim."},{"key":"273_CR31","doi-asserted-by":"crossref","first-page":"1133","DOI":"10.1016\/S0362-546X(00)00165-6","volume":"46","author":"M Torki","year":"2001","unstructured":"Torki, M.: Second-order directional derivatives of all eigenvalues of a symmetric matrix. Nonlinear Anal. Ser. A Methods 46, 1133\u20131150 (2001)","journal-title":"Nonlinear Anal. Ser. A Methods"},{"key":"273_CR32","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1006\/jmaa.1999.6320","volume":"234","author":"M Torki","year":"1999","unstructured":"Torki, M.: First- and second-order epi-differentiability in eigenvalue optimization. J. Math. Anal. Appl. 234, 391\u2013416 (1999)","journal-title":"J. Math. Anal. Appl."},{"key":"273_CR33","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1090\/S0002-9939-1955-0067842-9","volume":"6","author":"H Wielandt","year":"1955","unstructured":"Wielandt, H.: An extremum property of sums of eigenvalues. Proc. Amer. Math. Soc. 6, 106\u2013110 (1955)","journal-title":"Proc. Amer. Math. Soc."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-015-0273-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-015-0273-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-015-0273-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T04:59:08Z","timestamp":1559278748000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-015-0273-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,4]]},"references-count":33,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2015,9]]}},"alternative-id":["273"],"URL":"https:\/\/doi.org\/10.1007\/s10898-015-0273-8","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,3,4]]}}}