{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:47:42Z","timestamp":1776786462838,"version":"3.51.2"},"reference-count":67,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2019,2,18]],"date-time":"2019-02-18T00:00:00Z","timestamp":1550448000000},"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":["Math. Program."],"published-print":{"date-parts":[[2019,7]]},"DOI":"10.1007\/s10107-019-01364-5","type":"journal-article","created":{"date-parts":[[2019,2,18]],"date-time":"2019-02-18T14:53:47Z","timestamp":1550501627000},"page":"545-571","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Misspecified nonconvex statistical optimization for sparse phase retrieval"],"prefix":"10.1007","volume":"176","author":[{"given":"Zhuoran","family":"Yang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lin F.","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ethan X.","family":"Fang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tuo","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhaoran","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Matey","family":"Neykov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,2,18]]},"reference":[{"key":"1364_CR1","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1007\/978-3-319-51547-2_5","volume-title":"Geometric and Numerical Foundations of Movements","author":"AA Ahmadi","year":"2017","unstructured":"Ahmadi, A.A., Parrilo, P.A.: Some recent directions in algebraic methods for optimization and Lyapunov analysis. In: Laumond, J.P., Mansard, N., Lasserre, J.B. (eds.) Geometric and Numerical Foundations of Movements, pp. 89\u2013112. Springer, Cham (2017)"},{"key":"1364_CR2","first-page":"243","volume":"14","author":"P Alquier","year":"2013","unstructured":"Alquier, P., Biau, G.: Sparse single-index model. J. Mach. Learn. Res. 14, 243\u2013280 (2013)","journal-title":"J. Mach. Learn. Res."},{"key":"1364_CR3","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1007\/s10107-013-0701-9","volume":"146","author":"J Bolte","year":"2014","unstructured":"Bolte, J., Sabach, S., Teboulle, M.: Proximal alternating linearized minimization for nonconvex and nonsmooth problems. Math. Program. 146, 459\u2013494 (2014)","journal-title":"Math. Program."},{"key":"1364_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-20192-9","volume-title":"Statistics for High-Dimensional Data: Methods, Theory and Applications","author":"P B\u00fchlmann","year":"2011","unstructured":"B\u00fchlmann, P., van de Geer, S.: Statistics for High-Dimensional Data: Methods, Theory and Applications. Springer, Berlin (2011)"},{"key":"1364_CR5","doi-asserted-by":"publisher","first-page":"306","DOI":"10.1107\/S0108767307021903","volume":"63","author":"O Bunk","year":"2007","unstructured":"Bunk, O., Diaz, A., Pfeiffer, F., David, C., Schmitt, B., Satapathy, D.K., van der Veen, J.F.: Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels. Acta Crystallogr. Sect. A Found. Crystallogr. 63, 306\u2013314 (2007)","journal-title":"Acta Crystallogr. Sect. A Found. Crystallogr."},{"key":"1364_CR6","doi-asserted-by":"publisher","first-page":"2221","DOI":"10.1214\/16-AOS1443","volume":"44","author":"TT Cai","year":"2016","unstructured":"Cai, T.T., Li, X., Ma, Z.: Optimal rates of convergence for noisy sparse phase retrieval via thresholded Wirtinger flow. Ann. Stat. 44, 2221\u20132251 (2016)","journal-title":"Ann. Stat."},{"key":"1364_CR7","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1137\/151005099","volume":"57","author":"EJ Cand\u00e8s","year":"2015","unstructured":"Cand\u00e8s, E.J., Eldar, Y.C., Strohmer, T., Voroninski, V.: Phase retrieval via matrix completion. SIAM Rev. 57, 225\u2013251 (2015)","journal-title":"SIAM Rev."},{"key":"1364_CR8","doi-asserted-by":"publisher","first-page":"1985","DOI":"10.1109\/TIT.2015.2399924","volume":"61","author":"EJ Cand\u00e8s","year":"2015","unstructured":"Cand\u00e8s, E.J., Li, X., Soltanolkotabi, M.: Phase retrieval via Wirtinger flow: theory and algorithms. IEEE Trans. Inf. Theory 61, 1985\u20132007 (2015)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1364_CR9","doi-asserted-by":"publisher","first-page":"1241","DOI":"10.1002\/cpa.21432","volume":"66","author":"EJ Cand\u00e8s","year":"2013","unstructured":"Cand\u00e8s, E.J., Strohmer, T., Voroninski, V.: Phaselift: exact and stable signal recovery from magnitude measurements via convex programming. Commun. Pure Appl. Math. 66, 1241\u20131274 (2013)","journal-title":"Commun. Pure Appl. Math."},{"key":"1364_CR10","doi-asserted-by":"crossref","unstructured":"Chen, Y., Cand\u00e8s, E.: Solving random quadratic systems of equations is nearly as easy as solving linear systems. In: Advances in Neural Information Processing Systems (2015)","DOI":"10.1002\/cpa.21638"},{"key":"1364_CR11","doi-asserted-by":"publisher","first-page":"3743","DOI":"10.1103\/PhysRevLett.69.3743","volume":"69","author":"W Coene","year":"1992","unstructured":"Coene, W., Janssen, G., de Beeck, M.O., Van Dyck, D.: Phase retrieval through focus variation for ultra-resolution in field-emission transmission electron microscopy. Phys. Rev. Lett. 69, 3743 (1992)","journal-title":"Phys. Rev. Lett."},{"key":"1364_CR12","doi-asserted-by":"publisher","first-page":"410","DOI":"10.1198\/016214504000001501","volume":"100","author":"RD Cook","year":"2005","unstructured":"Cook, R.D., Ni, L.: Sufficient dimension reduction via inverse regression: a minimum discrepancy approach. J. Am. Stat. Assoc. 100, 410\u2013428 (2005)","journal-title":"J. Am. Stat. Assoc."},{"key":"1364_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-4948-7","volume-title":"A Mathematical Introduction to Compressive Sensing","author":"S Foucart","year":"2013","unstructured":"Foucart, S., Rauhut, H.: A Mathematical Introduction to Compressive Sensing. Springer, Berlin (2013)"},{"key":"1364_CR14","doi-asserted-by":"publisher","first-page":"1601","DOI":"10.1109\/TIT.2016.2642993","volume":"63","author":"M Genzel","year":"2017","unstructured":"Genzel, M.: High-dimensional estimation of structured signals from non-linear observations with general convex loss functions. IEEE Trans. Inf. Theory 63, 1601\u20131619 (2017)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1364_CR15","doi-asserted-by":"publisher","first-page":"2341","DOI":"10.1137\/120880811","volume":"23","author":"S Ghadimi","year":"2013","unstructured":"Ghadimi, S., Lan, G.: Stochastic first-and zeroth-order methods for nonconvex stochastic programming. SIAM J. Optim. 23, 2341\u20132368 (2013)","journal-title":"SIAM J. Optim."},{"key":"1364_CR16","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1007\/s10107-015-0871-8","volume":"156","author":"S Ghadimi","year":"2016","unstructured":"Ghadimi, S., Lan, G.: Accelerated gradient methods for nonconvex nonlinear and stochastic programming. Math. Program. 156, 59\u201399 (2016)","journal-title":"Math. Program."},{"key":"1364_CR17","unstructured":"Goldstein, L., Minsker, S., Wei, X.: Structured signal recovery from non-linear and heavy-tailed measurements (2016). arXiv preprint \n                    arXiv:1609.01025"},{"key":"1364_CR18","volume-title":"Matrix Computations","author":"GH Golub","year":"2012","unstructured":"Golub, G.H., Van Loan, C.F.: Matrix Computations. Johns Hopkins University Press, Johns Hopkins University Press (2012)"},{"key":"1364_CR19","unstructured":"Gon\u00e7alves, M.L., Melo, J.G., Monteiro, R.D.: Convergence rate bounds for a proximal admm with over-relaxation stepsize parameter for solving nonconvex linearly constrained problems (2017). arXiv preprint \n                    arXiv:1702.01850"},{"key":"1364_CR20","unstructured":"Gu, Q., Wang, Z., Liu, H.: Sparse PCA with oracle property. In: Advances in Neural Information Processing Systems (2014)"},{"key":"1364_CR21","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1016\/0304-4076(87)90030-3","volume":"35","author":"AK Han","year":"1987","unstructured":"Han, A.K.: Non-parametric analysis of a generalized regression model: the maximum rank correlation estimator. J. Econ. 35, 303\u2013316 (1987)","journal-title":"J. Econ."},{"key":"1364_CR22","doi-asserted-by":"publisher","first-page":"1046","DOI":"10.1364\/JOSAA.10.001046","volume":"10","author":"R Harrison","year":"1993","unstructured":"Harrison, R.: Phase problem in crystallography. J. Opt. Soc. Am. Part A Opt. Image Sci. 10, 1046\u20131055 (1993)","journal-title":"J. Opt. Soc. Am. Part A Opt. Image Sci."},{"key":"1364_CR23","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1137\/140990309","volume":"26","author":"M Hong","year":"2016","unstructured":"Hong, M., Luo, Z.-Q., Razaviyayn, M.: Convergence analysis of alternating direction method of multipliers for a family of nonconvex problems. SIAM J. Optim. 26, 337\u2013364 (2016)","journal-title":"SIAM J. Optim."},{"key":"1364_CR24","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-92870-8","volume-title":"Semiparametric and Nonparametric Methods in Econometrics","author":"JL Horowitz","year":"2009","unstructured":"Horowitz, J.L.: Semiparametric and Nonparametric Methods in Econometrics. Springer, Berlin (2009)"},{"key":"1364_CR25","unstructured":"Jaganathan, K., Eldar, Y.C. and Hassibi, B.: Phase retrieval: an overview of recent developments (2015). arXiv preprint \n                    arXiv:1510.07713"},{"key":"1364_CR26","doi-asserted-by":"publisher","first-page":"1751","DOI":"10.1214\/14-AOS1233","volume":"42","author":"B Jiang","year":"2014","unstructured":"Jiang, B., Liu, J.S.: Variable selection for general index models via sliced inverse regression. Ann. Stat. 42, 1751\u20131786 (2014)","journal-title":"Ann. Stat."},{"key":"1364_CR27","doi-asserted-by":"publisher","first-page":"682","DOI":"10.1198\/jasa.2009.0121","volume":"104","author":"IM Johnstone","year":"2009","unstructured":"Johnstone, I.M., Lu, A.Y.: On consistency and sparsity for principal components analysis in high dimensions. J. Am. Stat. Assoc. 104, 682\u2013693 (2009)","journal-title":"J. Am. Stat. Assoc."},{"key":"1364_CR28","unstructured":"Kakade, S.M., Kanade, V., Shamir, O., Kalai, A.: Efficient learning of generalized linear and single index models with isotonic regression. In: Advances in Neural Information Processing Systems (2011)"},{"key":"1364_CR29","unstructured":"Kalai, A.T., Sastry, R.: The isotron algorithm: high-dimensional isotonic regression. In: Conference on Learning Theory (2009)"},{"key":"1364_CR30","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/s10107-015-0874-5","volume":"156","author":"S Kim","year":"2016","unstructured":"Kim, S., Kojima, M., Toh, K.-C.: A Lagrangian-DNN relaxation: a fast method for computing tight lower bounds for a class of quadratic optimization problems. Math. Program. 156, 161\u2013187 (2016)","journal-title":"Math. Program."},{"key":"1364_CR31","doi-asserted-by":"publisher","first-page":"316","DOI":"10.1080\/01621459.1991.10475035","volume":"86","author":"K-C Li","year":"1991","unstructured":"Li, K.-C.: Sliced inverse regression for dimension reduction. J. Am. Stat. Assoc. 86, 316\u2013327 (1991)","journal-title":"J. Am. Stat. Assoc."},{"key":"1364_CR32","doi-asserted-by":"publisher","first-page":"1025","DOI":"10.1080\/01621459.1992.10476258","volume":"87","author":"K-C Li","year":"1992","unstructured":"Li, K.-C.: On principal Hessian directions for data visualization and dimension reduction: another application of Stein\u2019s lemma. J. Am. Stat. Assoc. 87, 1025\u20131039 (1992)","journal-title":"J. Am. Stat. Assoc."},{"key":"1364_CR33","doi-asserted-by":"publisher","first-page":"1009","DOI":"10.1214\/aos\/1176347254","volume":"17","author":"K-C Li","year":"1989","unstructured":"Li, K.-C., Duan, N.: Regression analysis under link violation. Ann. Stat. 17, 1009\u20131052 (1989)","journal-title":"Ann. Stat."},{"key":"1364_CR34","unstructured":"Li, X., Yang, L.F., Ge, J., Haupt, J., Zhang, T., Zhao, T.: On quadratic convergence of DC proximal Newton algorithm for nonconvex sparse learning in high dimensions (2017). arXiv preprint \n                    arXiv:1706.06066"},{"key":"1364_CR35","unstructured":"Lin, Q., Zhao, Z., Liu, J.S.: On consistency and sparsity for sliced inverse regression in high dimensions (2015). arXiv preprint \n                    arXiv:1507.03895"},{"key":"1364_CR36","first-page":"559","volume":"16","author":"P-L Loh","year":"2015","unstructured":"Loh, P.-L., Wainwright, M.J.: Regularized \n                    \n                      \n                    \n                    $${M}$$\n                    \n                      \n                        M\n                      \n                    \n                  -estimators with nonconvexity: statistical and algorithmic theory for local optima. J. Mach. Learn. Res. 16, 559\u2013616 (2015)","journal-title":"J. Mach. Learn. Res."},{"key":"1364_CR37","doi-asserted-by":"publisher","first-page":"615","DOI":"10.1007\/s10107-014-0800-2","volume":"152","author":"Z Lu","year":"2015","unstructured":"Lu, Z., Xiao, L.: On the complexity analysis of randomized block-coordinate descent methods. Math. Program. 152, 615\u2013642 (2015)","journal-title":"Math. Program."},{"key":"1364_CR38","doi-asserted-by":"publisher","first-page":"140101","DOI":"10.1103\/PhysRevB.68.140101","volume":"68","author":"S Marchesini","year":"2003","unstructured":"Marchesini, S., He, H., Chapman, H.N., Hau-Riege, S.P., Noy, A., Howells, M.R., Weierstall, U., Spence, J.C.: X-ray image reconstruction from a diffraction pattern alone. Phys. Rev. B 68, 140101 (2003)","journal-title":"Phys. Rev. B"},{"key":"1364_CR39","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-3242-6","volume-title":"Generalized Linear Models","author":"P McCullagh","year":"1989","unstructured":"McCullagh, P., Nelder, J.A.: Generalized Linear Models. Chapman and Hall, Boca Raton (1989)"},{"key":"1364_CR40","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1146\/annurev.physchem.59.032607.093642","volume":"59","author":"J Miao","year":"2008","unstructured":"Miao, J., Ishikawa, T., Shen, Q., Earnest, T.: Extending X-ray crystallography to allow the imaging of noncrystalline materials, cells, and single protein complexes. Ann. Rev. Phys. Chem. 59, 387\u2013410 (2008)","journal-title":"Ann. Rev. Phys. Chem."},{"key":"1364_CR41","doi-asserted-by":"publisher","first-page":"394","DOI":"10.1364\/JOSAA.7.000394","volume":"7","author":"R Millane","year":"1990","unstructured":"Millane, R.: Phase retrieval in crystallography and optics. J. Opt. Soc. Am. A Opt. Image Sci. 7, 394\u2013411 (1990)","journal-title":"J. Opt. Soc. Am. A Opt. Image Sci."},{"key":"1364_CR42","unstructured":"Netrapalli, P., Jain, P., Sanghavi, S.: Phase retrieval using alternating minimization. In: Advances in Neural Information Processing Systems (2013)"},{"key":"1364_CR43","unstructured":"Neykov, M., Wang, Z., Liu, H.: Agnostic estimation for misspecified phase retrieval models. In: Advances in Neural Information Processing Systems (2016)"},{"key":"1364_CR44","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1007\/s10107-003-0387-5","volume":"96","author":"PA Parrilo","year":"2003","unstructured":"Parrilo, P.A.: Semidefinite programming relaxations for semialgebraic problems. Math. Program. 96, 293\u2013320 (2003)","journal-title":"Math. Program."},{"key":"1364_CR45","doi-asserted-by":"publisher","first-page":"1528","DOI":"10.1109\/TIT.2016.2517008","volume":"62","author":"Y Plan","year":"2016","unstructured":"Plan, Y., Vershynin, R.: The generalized lasso with non-linear observations. IEEE Trans. Inf. Theory 62, 1528\u20131537 (2016)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1364_CR46","unstructured":"Plan, Y., Vershynin, R., Yudovina, E.: High-dimensional estimation with geometric constraints (2014). arXiv preprint \n                    arXiv:1404.3749"},{"key":"1364_CR47","doi-asserted-by":"publisher","first-page":"266","DOI":"10.1016\/j.jmva.2015.02.007","volume":"139","author":"P Radchenko","year":"2015","unstructured":"Radchenko, P.: High dimensional single index models. J. Multivar. Anal. 139, 266\u2013282 (2015)","journal-title":"J. Multivar. Anal."},{"key":"1364_CR48","doi-asserted-by":"publisher","first-page":"954","DOI":"10.1109\/31.85639","volume":"38","author":"H Sahinoglou","year":"1991","unstructured":"Sahinoglou, H., Cabrera, S.D.: On phase retrieval of finite-length sequences using the initial time sample. IEEE Trans. Circuits Syst. 38, 954\u2013958 (1991)","journal-title":"IEEE Trans. Circuits Syst."},{"key":"1364_CR49","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1109\/MSP.2014.2352673","volume":"32","author":"Y Shechtman","year":"2015","unstructured":"Shechtman, Y., Eldar, Y.C., Cohen, O., Chapman, H.N., Miao, J., Segev, M.: Phase retrieval with application to optical imaging: a contemporary overview. IEEE Signal Process. Mag. 32, 87\u2013109 (2015)","journal-title":"IEEE Signal Process. Mag."},{"key":"1364_CR50","doi-asserted-by":"publisher","first-page":"1135","DOI":"10.1214\/aos\/1176345632","volume":"9","author":"CM Stein","year":"1981","unstructured":"Stein, C.M.: Estimation of the mean of a multivariate normal distribution. Ann. Stat. 9, 1135\u20131151 (1981)","journal-title":"Ann. Stat."},{"key":"1364_CR51","doi-asserted-by":"crossref","unstructured":"Sun, J., Qu, Q., Wright, J.: A geometric analysis of phase retrieval. In: IEEE International Symposium on Information Theory (2016)","DOI":"10.1109\/ISIT.2016.7541725"},{"key":"1364_CR52","unstructured":"Sun, W., Wang, Z., Liu, H., Cheng, G.: Non-convex statistical optimization for sparse tensor graphical model. In: Advances in Neural Information Processing Systems (2015)"},{"key":"1364_CR53","unstructured":"Tan, K.M., Wang, Z., Liu, H., Zhang, T.: Sparse generalized eigenvalue problem: optimal statistical rates via truncated rayleigh flow (2016). arXiv preprint \n                    arXiv:1604.08697"},{"key":"1364_CR54","unstructured":"Thrampoulidis, C., Abbasi, E., Hassibi, B.: Lasso with non-linear measurements is equivalent to one with linear measurements. In: Advances in Neural Information Processing Systems (2015)"},{"key":"1364_CR55","unstructured":"Waldspurger, I.: Phase retrieval with random gaussian sensing vectors by alternating projections (2016). arXiv preprint \n                    arXiv:1609.03088"},{"key":"1364_CR56","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/s10107-013-0738-9","volume":"149","author":"I Waldspurger","year":"2015","unstructured":"Waldspurger, I., d\u00c1spremont, A., Mallat, S.: Phase recovery, maxcut and complex semidefinite programming. Math. Program. 149, 47\u201381 (2015)","journal-title":"Math. Program."},{"key":"1364_CR57","doi-asserted-by":"publisher","first-page":"2164","DOI":"10.1214\/14-AOS1238","volume":"42","author":"Z Wang","year":"2014","unstructured":"Wang, Z., Liu, H., Zhang, T.: Optimal computational and statistical rates of convergence for sparse nonconvex learning problems. Ann. Stat. 42, 2164\u20132201 (2014)","journal-title":"Ann. Stat."},{"key":"1364_CR58","unstructured":"Wang, Z., Lu, H., Liu, H.: Tighten after relax: Minimax-optimal sparse PCA in polynomial time. In: Advances in Neural Information Processing Systems (2014)"},{"key":"1364_CR59","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s12532-017-0121-6","volume":"10","author":"T Weisser","year":"2017","unstructured":"Weisser, T., Lasserre, J.-B., Toh, K.-C.: Sparse-BSOS: a bounded degree SOS hierarchy for large scale polynomial optimization with sparsity. Math. Program. Comput. 10, 1\u201332 (2017)","journal-title":"Math. Program. Comput."},{"issue":"2","key":"1364_CR60","doi-asserted-by":"publisher","first-page":"700","DOI":"10.1007\/s10915-017-0376-0","volume":"72","author":"Y Xu","year":"2017","unstructured":"Xu, Y., Yin, W.: A globally convergent algorithm for nonconvex optimization based on block coordinate update. J. Sci. Comput. 72(2), 700\u2013734 (2017)","journal-title":"J. Sci. Comput."},{"key":"1364_CR61","unstructured":"Yang, Z., Balasubramanian, K., Liu, H.: High-dimensional non-gaussian single index models via thresholded score function estimation (2017)"},{"key":"1364_CR62","unstructured":"Yang, Z., Wang, Z., Liu, H.: Estimating high-dimensional non-gaussian multiple index models via Stein\u2019s lemma. In: Advances in Neural Information Processing Systems (2017)"},{"key":"1364_CR63","unstructured":"Yang, Z., Wang, Z., Liu, H., Eldar, Y.C., Zhang, T.: Sparse nonlinear regression: Parameter estimation and asymptotic inference. In: International Conference on Machine Learning (2015)"},{"key":"1364_CR64","unstructured":"Yi, X., Wang, Z., Caramanis, C., Liu, H.: Optimal linear estimation under unknown nonlinear transform. In: Advances in Neural Information Processing Systems (2015)"},{"key":"1364_CR65","unstructured":"Zhang, H., Chi, Y., Liang, Y.: Provable nonconvex phase retrieval with outliers: median truncated Wirtinger flow. In: International Conference on Machine Learning (2016)"},{"issue":"1","key":"1364_CR66","doi-asserted-by":"publisher","first-page":"180","DOI":"10.1214\/17-AOS1547","volume":"46","author":"T Zhao","year":"2018","unstructured":"Zhao, T., Liu, H., Zhang, T.: Pathwise coordinate optimization for sparse learning: algorithm and theory. Ann. Stat. 46(1), 180\u2013218 (2018). \n                    https:\/\/doi.org\/10.1214\/17-AOS1547","journal-title":"Ann. Stat."},{"key":"1364_CR67","doi-asserted-by":"publisher","first-page":"630","DOI":"10.1198\/016214505000001285","volume":"101","author":"L Zhu","year":"2006","unstructured":"Zhu, L., Miao, B., Peng, H.: On sliced inverse regression with high-dimensional covariates. J. Am. Stat. Assoc. 101, 630\u2013643 (2006)","journal-title":"J. Am. Stat. Assoc."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-019-01364-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-019-01364-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-019-01364-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,2,18]],"date-time":"2020-02-18T16:14:28Z","timestamp":1582042468000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-019-01364-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,18]]},"references-count":67,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2019,7]]}},"alternative-id":["1364"],"URL":"https:\/\/doi.org\/10.1007\/s10107-019-01364-5","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,2,18]]},"assertion":[{"value":"22 November 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 January 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 February 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}