{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T08:17:52Z","timestamp":1774599472490,"version":"3.50.1"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2010,10,12]],"date-time":"2010-10-12T00:00:00Z","timestamp":1286841600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/2.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2011,3]]},"DOI":"10.1007\/s10107-010-0416-0","type":"journal-article","created":{"date-parts":[[2010,10,13]],"date-time":"2010-10-13T18:37:17Z","timestamp":1286995037000},"page":"123-144","source":"Crossref","is-referenced-by-count":32,"title":["Testing the nullspace property using semidefinite programming"],"prefix":"10.1007","volume":"127","author":[{"given":"Alexandre","family":"d\u2019Aspremont","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Laurent","family":"El Ghaoui","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2010,10,12]]},"reference":[{"issue":"1","key":"416_CR1","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/BF02187839","volume":"7","author":"F. Affentranger","year":"1992","unstructured":"Affentranger F., Schneider R.: Random projections of regular simplices. Discrete Comput. Geom. 7(1), 219\u2013226 (1992)","journal-title":"Discrete Comput. Geom."},{"issue":"2","key":"416_CR2","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1007\/s10208-005-0178-x","volume":"7","author":"A. Barvinok","year":"2007","unstructured":"Barvinok A.: Integration and optimization of multivariate polynomials by restriction onto a random subspace. Foundations Comput. Math. 7(2), 229\u2013244 (2007)","journal-title":"Foundations Comput. Math."},{"key":"416_CR3","doi-asserted-by":"crossref","unstructured":"Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear matrix inequalities in system and control theory. SIAM (1994)","DOI":"10.1137\/1.9781611970777"},{"issue":"12","key":"416_CR4","doi-asserted-by":"publisher","first-page":"5406","DOI":"10.1109\/TIT.2006.885507","volume":"52","author":"E. Cand\u00e8s","year":"2006","unstructured":"Cand\u00e8s E., Tao T.: Near-optimal signal recovery from random projections: universal encoding strategies?. IEEE Trans. Inform. Theory 52(12), 5406\u20135425 (2006)","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"12","key":"416_CR5","doi-asserted-by":"publisher","first-page":"4203","DOI":"10.1109\/TIT.2005.858979","volume":"51","author":"E.J. Cand\u00e8s","year":"2005","unstructured":"Cand\u00e8s E.J., Tao T.: Decoding by linear programming. IEEE Trans. Inform. Theory 51(12), 4203\u20134215 (2005)","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"1","key":"416_CR6","first-page":"211","volume":"22","author":"A. Cohen","year":"2009","unstructured":"Cohen A., Dahmen W., DeVore R.: Compressed sensing and best k-term approximation. J. AMS 22(1), 211\u2013231 (2009)","journal-title":"J. AMS"},{"issue":"3","key":"416_CR7","doi-asserted-by":"publisher","first-page":"434","DOI":"10.1137\/050645506","volume":"49","author":"A. d\u2019Aspremont","year":"2007","unstructured":"d\u2019Aspremont A., El Ghaoui L., Jordan M., Lanckriet G.R.G.: A direct formulation for sparse PCA using semidefinite programming. SIAM Rev. 49(3), 434\u2013448 (2007)","journal-title":"SIAM Rev."},{"key":"416_CR8","first-page":"1269","volume":"9","author":"A. d\u2019Aspremont","year":"2008","unstructured":"d\u2019Aspremont A., Bach F., El Ghaoui L.: Optimal solutions for sparse principal component analysis. J. Mach. Learn. Res. 9, 1269\u20131294 (2008)","journal-title":"J. Mach. Learn. Res."},{"issue":"7","key":"416_CR9","doi-asserted-by":"publisher","first-page":"2845","DOI":"10.1109\/18.959265","volume":"47","author":"D. Donoho","year":"2001","unstructured":"Donoho D., Huo X.: Uncertainty principles and ideal atomic decomposition. IEEE Trans. Inform. Theory 47(7), 2845\u20132862 (2001)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"416_CR10","first-page":"08073590","volume":"arXiv","author":"D. Donoho","year":"2008","unstructured":"Donoho D., Tanner J.: Counting the faces of randomly-projected hypercubes and orthants, with applications. Arxiv Preprint arXiv, 08073590 (2008)","journal-title":"Arxiv Preprint"},{"issue":"27","key":"416_CR11","doi-asserted-by":"publisher","first-page":"9446","DOI":"10.1073\/pnas.0502269102","volume":"102","author":"D.L. Donoho","year":"2005","unstructured":"Donoho D.L., Tanner J.: Sparse nonnegative solutions of underdetermined linear equations by linear programming. Proc. Natl. Acad. Sci. 102(27), 9446\u20139451 (2005)","journal-title":"Proc. Natl. Acad. Sci."},{"key":"416_CR12","doi-asserted-by":"publisher","first-page":"1115","DOI":"10.1145\/227683.227684","volume":"42","author":"M. Goemans","year":"1995","unstructured":"Goemans M., Williamson D.: Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J ACM 42, 1115\u20131145 (1995)","journal-title":"J ACM"},{"key":"416_CR13","doi-asserted-by":"crossref","unstructured":"Ibragimov, I., Sudakov, V., Tsirelson, B.: Norms of Gaussian sample functions. In: Proceedings of the third Japan USSR symposium on probability theory, lecture notes in math, vol. 550, pp. 20\u201341 (1976)","DOI":"10.1007\/BFb0077482"},{"key":"416_CR14","unstructured":"Juditsky, A., Nemirovski, A.: On verifiable sufficient conditions for sparse signal recovery via \u2113\n                           1 minimization. ArXiv 08092650 (2008)"},{"key":"416_CR15","unstructured":"Lee, K., Bresler, Y.: Computing performance guarantees for compressed sensing. In: IEEE International Conference on Acoustics, Speech and Signal Processing, 2008. ICASSP 2008, pp 5129\u20135132 (2008)"},{"key":"416_CR16","unstructured":"Massart, P.: Concentration inequalities and model selection. Ecole d\u2019Et\u00e9 de Probabilit\u00e9s de Saint-Flour XXXIII (2007)"},{"issue":"1","key":"416_CR17","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1137\/S00361445024180","volume":"45","author":"C. Moler","year":"2003","unstructured":"Moler C., Van Loan C.: Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Rev. 45(1), 3\u201349 (2003)","journal-title":"SIAM Rev."},{"key":"416_CR18","volume-title":"Introductory Lectures on Convex Optimization","author":"Y. Nesterov","year":"2003","unstructured":"Nesterov Y.: Introductory Lectures on Convex Optimization. Springer, Heidelberg (2003)"},{"issue":"1","key":"416_CR19","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1007\/s10107-004-0552-5","volume":"103","author":"Y. Nesterov","year":"2005","unstructured":"Nesterov Y.: Smooth minimization of non-smooth functions. Math. Program. 103(1), 127\u2013152 (2005)","journal-title":"Math. Program."},{"issue":"2","key":"416_CR20","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1007\/s10107-006-0001-8","volume":"110","author":"Y. Nesterov","year":"2007","unstructured":"Nesterov Y.: Smoothing technique and its applications in semidefinite optimization. Math. Program. 110(2), 245\u2013259 (2007)","journal-title":"Math. Program."},{"key":"416_CR21","doi-asserted-by":"publisher","first-page":"625","DOI":"10.1080\/10556789908805766","volume":"11","author":"J. Sturm","year":"1999","unstructured":"Sturm J.: Using SEDUMI 1.0x, a MATLAB toolbox for optimization over symmetric cones. Optim. Method. Sofw. 11, 625\u2013653 (1999)","journal-title":"Optim. Method. Sofw."},{"key":"416_CR22","doi-asserted-by":"publisher","first-page":"545","DOI":"10.1080\/10556789908805762","volume":"11","author":"K.C. Toh","year":"1999","unstructured":"Toh K.C., Todd M.J., Tutuncu R.H.: SDPT3\u2014a MATLAB software package for semidefinite programming. Optim. Method. Sofw. 11, 545\u2013581 (1999)","journal-title":"Optim. Method. Sofw."},{"issue":"2","key":"416_CR23","first-page":"181","volume":"11","author":"A. Vershik","year":"1992","unstructured":"Vershik A., Sporyshev P.: Asymptotic behavior of the number of faces of random polyhedra and the neighborliness problem. Selecta Math Soviet 11(2), 181\u2013201 (1992)","journal-title":"Selecta Math Soviet"},{"key":"416_CR24","unstructured":"Zhang Y.: A simple proof for recoverability of \u2113\n                           1-minimization: Go over or under. Rice University CAAM Technical report TR05-09 (2005)"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-010-0416-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-010-0416-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-010-0416-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-010-0416-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,7]],"date-time":"2019-04-07T11:23:47Z","timestamp":1554636227000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-010-0416-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,10,12]]},"references-count":24,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,3]]}},"alternative-id":["416"],"URL":"https:\/\/doi.org\/10.1007\/s10107-010-0416-0","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,10,12]]}}}