{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,26]],"date-time":"2025-10-26T14:10:58Z","timestamp":1761487858263},"reference-count":34,"publisher":"Elsevier BV","issue":"6","license":[{"start":{"date-parts":[[2004,1,1]],"date-time":"2004-01-01T00:00:00Z","timestamp":1072915200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["European Journal of Control"],"published-print":{"date-parts":[[2004,1]]},"DOI":"10.3166\/ejc.10.527-538","type":"journal-article","created":{"date-parts":[[2007,6,14]],"date-time":"2007-06-14T15:08:07Z","timestamp":1181833687000},"page":"527-538","source":"Crossref","is-referenced-by-count":52,"title":["A Spectral Quadratic-SDP Method with Applications to Fixed-Order H2 and H\u221e Synthesis"],"prefix":"10.1016","volume":"10","author":[{"given":"Pierre","family":"Apkarian","sequence":"first","affiliation":[]},{"given":"Dominikus","family":"Noll","sequence":"additional","affiliation":[]},{"given":"Jean-Baptiste","family":"Thevenet","sequence":"additional","affiliation":[]},{"given":"Hoang","family":"Duong Tuan","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.3166\/ejc.10.527-538_bib0005","series-title":"Network analysis and synthesis: a modern systems theory approach","author":"Anderson","year":"1973"},{"key":"10.3166\/ejc.10.527-538_bib0010","author":"Apkarian","year":"2005","journal-title":"Nonsmooth H\u221e synthesis"},{"key":"10.3166\/ejc.10.527-538_bib0015","series-title":"Proceedings of the IFAC Conference on System Structure and Control","article-title":"Controller design via nonsmooth multi-directional search","author":"Apkarian","year":"2004"},{"key":"10.3166\/ejc.10.527-538_bib0020","doi-asserted-by":"crossref","first-page":"1137","DOI":"10.1002\/rnc.807","article-title":"Fixed-order H\u221e control design via an augmented Lagrangian method","volume":"13","author":"Apkarian","year":"2003","journal-title":"Int J Robust Nonlinear Control"},{"key":"10.3166\/ejc.10.527-538_bib0025","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1023\/A:1008385006172","article-title":"Concave programming in control theory","volume":"15","author":"Apkarian","year":"1999","journal-title":"J Global Optim"},{"key":"10.3166\/ejc.10.527-538_bib0030","series-title":"Nonlinear programming","author":"Bertsekas","year":"1995"},{"key":"10.3166\/ejc.10.527-538_bib0035","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0962492900002518","article-title":"Sequential quadratic programming","author":"Boggs","year":"1995","journal-title":"Acta Numerica"},{"key":"10.3166\/ejc.10.527-538_bib0040","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/BF01204181","article-title":"Local analysis of Newton-type methods for variational inequalitites and nonlinear programming","volume":"29","author":"Bonnans","year":"1994","journal-title":"Appl Math Optim"},{"key":"10.3166\/ejc.10.527-538_bib0045","series-title":"H\u221e Control and its applications, Lectures Notes in Control and Information Sciences No. 235","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-84628-529-5","author":"Chen","year":"1998"},{"key":"10.3166\/ejc.10.527-538_bib0050","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1137\/0728030","article-title":"A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds","volume":"28","author":"Conn","year":"1991","journal-title":"SIAM J Numer Anal"},{"key":"10.3166\/ejc.10.527-538_bib0055","unstructured":"Conn AR, Gould NIM, Sartenaer A, Toint PL. Local convergence properties of two augmented Lagrangian algorithms for optimization with a combination of general equality and linear constraints. Technical Report TR\/PA\/93\/27, CERFACS, Toulouse, France, 1993"},{"key":"10.3166\/ejc.10.527-538_bib0060","doi-asserted-by":"crossref","first-page":"674","DOI":"10.1137\/S1052623493251463","article-title":"Convergence properties of an augmented Lagrangian algorithm for optimization with a combination of general equality and linear constraints","volume":"6","author":"Conn","year":"1996","journal-title":"SIAM J Optim"},{"key":"10.3166\/ejc.10.527-538_bib0065","series-title":"Trust-region methods, MPS\/SIAM Series on Optimization","author":"Conn","year":"2000"},{"key":"10.3166\/ejc.10.527-538_bib0070","doi-asserted-by":"crossref","first-page":"348","DOI":"10.1080\/00207170010010605","article-title":"An augmented Lagrangian method for a class of LMI-constrained problems in robust control theory","volume":"74","author":"Fares","year":"2001","journal-title":"Int J Control"},{"key":"10.3166\/ejc.10.527-538_bib0075","doi-asserted-by":"crossref","first-page":"1791","DOI":"10.1137\/S0363012900373483","article-title":"Robust control via sequential semidefinite programming","volume":"40","author":"Fares","year":"2002","journal-title":"SIAM J Control Optim"},{"key":"10.3166\/ejc.10.527-538_bib0080","series-title":"Practical methods of optimization","author":"Fletcher","year":"1987"},{"key":"10.3166\/ejc.10.527-538_bib0085","doi-asserted-by":"crossref","unstructured":"Gahinet P. Reliable computation of H\u221e central controllers near the optimum. Technical Report 13, INRIA, Domaine de Voluceau, Rocquencourt, 78150, Le Chesnay, France, 1992","DOI":"10.23919\/ACC.1992.4792171"},{"key":"10.3166\/ejc.10.527-538_bib0090","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1002\/rnc.4590040403","article-title":"A linear matrix inequality approach to H\u221e control","volume":"4","author":"Gahinet","year":"1994","journal-title":"Int J Robust Nonlinear Control"},{"key":"10.3166\/ejc.10.527-538_bib0095","series-title":"LMI control toolbox","author":"Gahinet","year":"1995"},{"key":"10.3166\/ejc.10.527-538_bib0100","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1109\/TAC.1986.1104161","article-title":"Application of modern synthesis to aircraft control: three case studies","volume":"AC-31","author":"Gangsaas","year":"1986","journal-title":"IEEE Trans Autom Control"},{"key":"10.3166\/ejc.10.527-538_bib0105","series-title":"Proceedings of the IEEE Conference on Decision and Control","first-page":"3609","article-title":"Coordinate optimization for bi-convex matrix inequalitites","author":"Helton","year":"1997"},{"key":"10.3166\/ejc.10.527-538_bib0110","series-title":"Multivariable feedback: a classical approach. Lectures Notes in Control and Information Sciences","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0043756","author":"Hung","year":"1982"},{"key":"10.3166\/ejc.10.527-538_bib0115","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1109\/9.362","article-title":"Robust control with structured perturbations","volume":"36","author":"Keel","year":"1988","journal-title":"IEEE Trans Autom Control"},{"key":"10.3166\/ejc.10.527-538_bib0120","unstructured":"Leibfritz F. Computational design of stabilizing static output feedback controller. Technical Report Mathematik\/Informatik, Forschungsbericht 99-02, Universit\u00e4t Trier, 1998"},{"key":"10.3166\/ejc.10.527-538_bib0125","doi-asserted-by":"crossref","first-page":"576","DOI":"10.1287\/moor.21.3.576","article-title":"Derivatives of spectral functions","volume":"21","author":"Lewis","year":"1996","journal-title":"Math Oper Res"},{"key":"10.3166\/ejc.10.527-538_bib0130","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1137\/S089547980036838X","article-title":"Twice differentiable spectral functions","volume":"23","author":"Lewis","year":"2001","journal-title":"SIAM J Matrix Anal Appl"},{"key":"10.3166\/ejc.10.527-538_bib0135","series-title":"Proceedings of the American Control Conference","article-title":"Solving a class of rank minimization problems via semi-definite programs, with applications to the fixed order output feedback synthesis","author":"Mesbahi","year":"1997"},{"key":"10.3166\/ejc.10.527-538_bib0140","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1080\/10556780008805787","article-title":"Penalty\/barrier multiplier algorithm for semidefinite programming","volume":"13","author":"Mosheyev","year":"2000","journal-title":"Optim Meth Software"},{"key":"10.3166\/ejc.10.527-538_bib0145","article-title":"Spectral bundle methods for non-convex maximum eigenvalue functions. Part 1: First-order methods","author":"Noll","year":"2005","journal-title":"Math Program B"},{"key":"10.3166\/ejc.10.527-538_bib0150","article-title":"Spectral bundle methods for nonconvex maximum eigenvalue functions. Part 2: Secondorder methods","author":"Noll","year":"2005","journal-title":"Math Program B"},{"key":"10.3166\/ejc.10.527-538_bib0155","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1137\/S1052623402413963","article-title":"Partially augmented Lagrangian method for matrix inequality constraints","volume":"15","author":"Noll","year":"2004","journal-title":"SIAM J Optim"},{"key":"10.3166\/ejc.10.527-538_bib0160","author":"Shapiro","year":"2002"},{"key":"10.3166\/ejc.10.527-538_bib0165","unstructured":"Sturm JF. Using SeDuMi 1.02, a Matlab toolbox for optimization over symmetric cones. Technical report, Tilburg University, Tilburg, Netherlands, October 2001"},{"key":"10.3166\/ejc.10.527-538_bib0170","series-title":"Nonlinear spectral SDP method for BMI-constrained problems: applications to control design. To appear in Informatics in Control Automation and Robotics","author":"Thevenet","year":"2005"}],"container-title":["European Journal of Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0947358004703982?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0947358004703982?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,4,28]],"date-time":"2019-04-28T22:51:02Z","timestamp":1556491862000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0947358004703982"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,1]]},"references-count":34,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2004,1]]}},"alternative-id":["S0947358004703982"],"URL":"https:\/\/doi.org\/10.3166\/ejc.10.527-538","relation":{},"ISSN":["0947-3580"],"issn-type":[{"value":"0947-3580","type":"print"}],"subject":[],"published":{"date-parts":[[2004,1]]}}}