{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T09:14:14Z","timestamp":1723108454607},"reference-count":52,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2013,9,20]],"date-time":"2013-09-20T00:00:00Z","timestamp":1379635200000},"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":[[2014,3]]},"DOI":"10.1007\/s10589-013-9602-3","type":"journal-article","created":{"date-parts":[[2013,9,19]],"date-time":"2013-09-19T19:33:02Z","timestamp":1379619182000},"page":"271-306","source":"Crossref","is-referenced-by-count":8,"title":["An infeasible-point subgradient method using adaptive approximate projections"],"prefix":"10.1007","volume":"57","author":[{"given":"Dirk A.","family":"Lorenz","sequence":"first","affiliation":[]},{"given":"Marc E.","family":"Pfetsch","sequence":"additional","affiliation":[]},{"given":"Andreas M.","family":"Tillmann","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2013,9,20]]},"reference":[{"key":"9602_CR1","first-page":"23","volume":"81","author":"Y.I. Alber","year":"1998","unstructured":"Alber, Y.I., Iusem, A.N., Solodov, M.V.: On the projected subgradient method for nonsmooth convex optimization in a Hilbert space. Math. Program. 81, 23\u201335 (1998)","journal-title":"Math. Program."},{"key":"9602_CR2","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1007\/BF02591740","volume":"37","author":"E. Allen","year":"1987","unstructured":"Allen, E., Helgason, R., Kennington, J., Shetty, B.: A generalization of Polyak\u2019s convergence result for subgradient optimization. Math. Program. 37, 309\u2013317 (1987)","journal-title":"Math. Program."},{"key":"9602_CR3","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1007\/s10107-007-0148-y","volume":"120","author":"K.M. Anstreicher","year":"2009","unstructured":"Anstreicher, K.M., Wolsey, L.A.: Two \u201cwell-known\u201d properties of subgradient optimization. Math. Program. 120, 213\u2013220 (2009)","journal-title":"Math. Program."},{"key":"9602_CR4","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1137\/S0036144593251710","volume":"38","author":"H.H. Bauschke","year":"1996","unstructured":"Bauschke, H.H., Borwein, J.M.: On projection algorithms for solving convex feasibility problems. SIAM Rev. 38, 367\u2013426 (1996)","journal-title":"SIAM Rev."},{"key":"9602_CR5","doi-asserted-by":"crossref","first-page":"380","DOI":"10.1016\/0377-2217(81)90096-5","volume":"7","author":"M.S. Bazaraa","year":"1981","unstructured":"Bazaraa, M.S., Sherali, H.D.: On the choice of step size in subgradient optimization. Eur. J. Oper. Res. 7, 380\u2013388 (1981)","journal-title":"Eur. J. Oper. Res."},{"key":"9602_CR6","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1137\/0311049","volume":"11","author":"D.P. Bertsekas","year":"1973","unstructured":"Bertsekas, D.P., Mitter, S.K.: A descent numerical method for optimization problems with nondifferentiable cost functionals. SIAM J. Control 11, 637\u2013652 (1973)","journal-title":"SIAM J. Control"},{"key":"9602_CR7","series-title":"Ser. Oper. Res.","volume-title":"Introduction to Stochastic Programming","author":"J.R. Birge","year":"1999","unstructured":"Birge, J.R., Louveaux, F.: Introduction to Stochastic Programming. Ser. Oper. Res. Springer, Berlin (1999). Corrected second printing"},{"key":"9602_CR8","series-title":"Lecture Notes","volume-title":"Stochastic Subgradient Methods","author":"S. Boyd","year":"2007","unstructured":"Boyd, S., Mutapcic, A.: In: Stochastic Subgradient Methods. Lecture Notes (2007). http:\/\/see.stanford.edu\/materials\/lsocoee364b\/04-stoch_subgrad_notes.pdf . Accessed 08\/29\/2013"},{"key":"9602_CR9","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1137\/060657704","volume":"51","author":"A.M. Bruckstein","year":"2009","unstructured":"Bruckstein, A.M., Donoho, D.L., Elad, M.: From sparse solutions of systems of equations to sparse modeling of signals and images. SIAM Rev. 51, 34\u201381 (2009)","journal-title":"SIAM Rev."},{"key":"9602_CR10","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1109\/TIT.2005.862083","volume":"52","author":"E. Cand\u00e8s","year":"2006","unstructured":"Cand\u00e8s, E., Romberg, J., Tao, T.: Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory 52, 489\u2013509 (2006)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9602_CR11","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1287\/mnsc.6.1.73","volume":"6","author":"A. Charnes","year":"1959","unstructured":"Charnes, A., Cooper, W.W.: Chance-constrained programming. Manag. Sci. 6, 73\u201379 (1959)","journal-title":"Manag. Sci."},{"key":"9602_CR12","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1137\/S1064827596304010","volume":"20","author":"S.S. Chen","year":"1998","unstructured":"Chen, S.S., Donoho, D.L., Saunders, M.A.: Atomic decomposition by basis pursuit. SIAM J. Sci. Comput. 20, 33\u201361 (1998)","journal-title":"SIAM J. Sci. Comput."},{"key":"9602_CR13","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1007\/s102080010027","volume":"2","author":"A. Cohen","year":"2002","unstructured":"Cohen, A., Dahmen, W., DeVore, R.: Adaptive wavelet methods. II. Beyond the elliptic case. Found. Comput. Math. 2, 203\u2013245 (2002)","journal-title":"Found. Comput. Math."},{"key":"9602_CR14","doi-asserted-by":"crossref","first-page":"1295","DOI":"10.1109\/TIP.2002.804527","volume":"11","author":"P.L. Combettes","year":"2002","unstructured":"Combettes, P.L., Luo, J.: An adaptive level set method for nondifferentiable constrained image recovery. IEEE Trans. Image Process. 11, 1295\u20131304 (2002)","journal-title":"IEEE Trans. Image Process."},{"key":"9602_CR15","unstructured":"Compressive sensing resources. http:\/\/dsp.rice.edu\/cs . Accessed 08\/29\/2013"},{"key":"9602_CR16","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1137\/080718814","volume":"20","author":"G. D\u2019Antonio","year":"2009","unstructured":"D\u2019Antonio, G., Frangioni, A.: Convergence analysis of deflected conditional approximate subgradient methods. SIAM J. Optim. 20, 357\u2013386 (2009)","journal-title":"SIAM J. Optim."},{"key":"9602_CR17","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1109\/TIT.2006.871582","volume":"52","author":"D.L. Donoho","year":"2006","unstructured":"Donoho, D.L.: Compressed sensing. IEEE Trans. Inf. Theory 52, 1289\u20131306 (2006)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9602_CR18","unstructured":"Ferris, M.C.: Weak sharp minima and exact penalty functions. Tech. rep. 779, Comp. Sci. Dept., University of Wisconsin, Madison, WI, USA (1988)"},{"key":"9602_CR19","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/s101070050053","volume":"85","author":"J.L. Goffin","year":"1999","unstructured":"Goffin, J.L., Kiwiel, K.: Convergence of a simple subgradient level method. Math. Program. 85, 207\u2013211 (1999)","journal-title":"Math. Program."},{"key":"9602_CR20","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1002\/cpa.20350","volume":"64","author":"M. Grasmair","year":"2011","unstructured":"Grasmair, M., Haltmeier, M., Scherzer, O.: Necessary and sufficient conditions for linear convergence of \u2113 1-regularization. Commun. Pure Appl. Math. 64, 161\u2013182 (2011)","journal-title":"Commun. Pure Appl. Math."},{"key":"9602_CR21","series-title":"Lecture Notes in Economics and Mathematical Systems","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-51697-9","volume-title":"Duality in Stochastic Linear and Dynamic Programming","author":"W.K. Klein Haneveld","year":"1986","unstructured":"Klein Haneveld, W.K.: Duality in Stochastic Linear and Dynamic Programming. Lecture Notes in Economics and Mathematical Systems, vol.\u00a0274. Springer, Berlin (1986)"},{"key":"9602_CR22","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1007\/s10287-005-0007-3","volume":"3","author":"W.K. Klein Haneveld","year":"2006","unstructured":"Klein Haneveld, W.K., van der Vlerk, M.H.: Integrated chance constraints: reduced forms and an algorithm. Comput. Manag. Sci. 3, 245\u2013269 (2006)","journal-title":"Comput. Manag. Sci."},{"key":"9602_CR23","doi-asserted-by":"crossref","first-page":"1547","DOI":"10.1137\/070711712","volume":"20","author":"E.S.H. Neto","year":"2009","unstructured":"Neto, E.S.H., De Pierro, A.R.: Incremental subgradients for constrainted convex optimization: a unified framework and new methods. SIAM J. Optim. 20, 1547\u20131572 (2009)","journal-title":"SIAM J. Optim."},{"key":"9602_CR24","doi-asserted-by":"crossref","first-page":"409","DOI":"10.6028\/jres.049.044","volume":"49","author":"M.R. Hestenes","year":"1952","unstructured":"Hestenes, M.R., Stiefel, E.: Methods of conjugate gradients for solving linear systems. J. Res. Natl. Bur. Stand. 49, 409\u2013436 (1952)","journal-title":"J. Res. Natl. Bur. Stand."},{"key":"9602_CR25","series-title":"Ser. Grundlehren der Mathematischen Wissenschaften [Fundam. Princ. Math. Sci.]","volume-title":"Convex Analysis and Minimization Algorithms. II","author":"J.-B. Hiriart-Urruty","year":"1993","unstructured":"Hiriart-Urruty, J.-B., Lemar\u00e9chal, C.: Convex Analysis and Minimization Algorithms. II. Ser. Grundlehren der Mathematischen Wissenschaften [Fundam. Princ. Math. Sci.], vol.\u00a0306. Springer, Berlin (1993)"},{"key":"9602_CR26","volume-title":"Fundamentals of Convex Analysis","author":"J.-B. Hiriart-Urruty","year":"2004","unstructured":"Hiriart-Urruty, J.-B., Lemar\u00e9chal, C.: Fundamentals of Convex Analysis. Springer, Berlin (2004). Corrected second printing"},{"key":"9602_CR27","volume-title":"Stochastic Linear Programming. Models, Theory, and Computation","author":"P. Kall","year":"2005","unstructured":"Kall, P., Mayer, J.: Stochastic Linear Programming. Models, Theory, and Computation. Springer, Berlin (2005)"},{"key":"9602_CR28","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1007\/BF01588797","volume":"49","author":"S. Kim","year":"1991","unstructured":"Kim, S., Ahn, H., Cho, S.-C.: Variable target value subgradient method. Math. Program. 49, 359\u2013369 (1991)","journal-title":"Math. Program."},{"key":"9602_CR29","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1007\/BF01585731","volume":"46","author":"K.C. Kiwiel","year":"1990","unstructured":"Kiwiel, K.C.: Proximity control in bundle methods for convex nondifferentiable minimization. Math. Program. 46, 105\u2013122 (1990)","journal-title":"Math. Program."},{"key":"9602_CR30","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1023\/A:1022671302532","volume":"96","author":"K.C. Kiwiel","year":"1998","unstructured":"Kiwiel, K.C.: Subgradient method with entropic projections for convex nondifferentiable minimization. J. Optim. Theory Appl. 96, 159\u2013173 (1998)","journal-title":"J. Optim. Theory Appl."},{"key":"9602_CR31","doi-asserted-by":"crossref","first-page":"807","DOI":"10.1137\/S1052623400376366","volume":"14","author":"K.C. Kiwiel","year":"2004","unstructured":"Kiwiel, K.C.: Convergence of approximate and incremental subgradient methods for convex optimization. SIAM J. Optim. 14, 807\u2013840 (2004)","journal-title":"SIAM J. Optim."},{"key":"9602_CR32","unstructured":"Kruschel, C., Lorenz, D.A.: Computing and analyzing recoverable supports for sparse reconstruction (2013). arXiv:1309.2460 [math.OC]"},{"key":"9602_CR33","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1007\/s10957-008-9476-1","volume":"141","author":"D. Kuhn","year":"2009","unstructured":"Kuhn, D.: Convergent bounds for stochastic programs with expected value constraints. J. Optim. Theory Appl. 141, 597\u2013618 (2009)","journal-title":"J. Optim. Theory Appl."},{"key":"9602_CR34","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1016\/0377-2217(94)00200-2","volume":"88","author":"T. Larsson","year":"1996","unstructured":"Larsson, T., Patriksson, M., Str\u00f6mberg, A.-B.: Conditional subgradient optimization\u2014theory and applications. Eur. J. Oper. Res. 88, 382\u2013403 (1996)","journal-title":"Eur. J. Oper. Res."},{"key":"9602_CR35","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1007\/s10208-008-9036-y","volume":"9","author":"A.S. Lewis","year":"2009","unstructured":"Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Found. Comput. Math. 9, 485\u2013513 (2009)","journal-title":"Found. Comput. Math."},{"key":"9602_CR36","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1007\/s10589-005-3914-x","volume":"34","author":"C. Lim","year":"2005","unstructured":"Lim, C., Sherali, H.D.: Convergence and computational analyses for some variable target value and subgradient deflection methods. Comput. Optim. Appl. 34, 409\u2013428 (2005)","journal-title":"Comput. Optim. Appl."},{"key":"9602_CR37","unstructured":"L\u00f6bel, A.: Optimal vehicle scheduling in public transit. Dissertation, Technische Universit\u00e4t Berlin (1998)"},{"key":"9602_CR38","unstructured":"Lorenz, D.A., Pfetsch, M.E., Tillmann, A.M.: Solving Basis Pursuit: Subgradient algorithm, heuristic optimality check, and solver comparison. Optimization Online E-Print ID 2011-07-3100 (2011)"},{"key":"9602_CR39","first-page":"733","volume-title":"Proc. ICASSP\u201905","author":"D. Malioutov","year":"2005","unstructured":"Malioutov, D., \u00c7etin, M., Willsky, A.: Homotopy continuation for sparse signal representation. In: Proc. ICASSP\u201905, vol.\u00a05, pp.\u00a0733\u2013736 (2005)"},{"key":"9602_CR40","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1137\/S1052623499362111","volume":"12","author":"A. Nedi\u0107","year":"2001","unstructured":"Nedi\u0107, A., Bertsekas, D.P.: Incremental subgradient methods for nondifferentiable optimization. SIAM J. Optim. 12, 109\u2013138 (2001)","journal-title":"SIAM J. Optim."},{"key":"9602_CR41","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1007\/s10107-008-0262-5","volume":"125","author":"A. Nedi\u0107","year":"2010","unstructured":"Nedi\u0107, A., Bertsekas, D.P.: The effect of deterministic noise in subgradient methods. Math. Program. 125, 75\u201399 (2010)","journal-title":"Math. Program."},{"key":"9602_CR42","doi-asserted-by":"crossref","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, 127\u2013152 (2005)","journal-title":"Math. Program."},{"key":"9602_CR43","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1093\/imanum\/20.3.389","volume":"20","author":"M. Osbourne","year":"2000","unstructured":"Osbourne, M., Presnell, B., Turlach, B.: A new approach to variable selection in least squares problems. IMA J. Numer. Anal. 20, 389\u2013402 (2000)","journal-title":"IMA J. Numer. Anal."},{"key":"9602_CR44","first-page":"33","volume":"174","author":"B.T. Polyak","year":"1967","unstructured":"Polyak, B.T.: A general method for solving extremal problems. Dokl. Akad. Nauk SSSR 174, 33\u201336 (1967)","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"9602_CR45","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/0041-5553(69)90061-5","volume":"9","author":"B.T. Polyak","year":"1969","unstructured":"Polyak, B.T.: Minimization of nonsmooth functionals. USSR Comput. Math. Math. Phys. 9, 14\u201329 (1969)","journal-title":"USSR Comput. Math. Math. Phys."},{"key":"9602_CR46","series-title":"Ser. IIASA Proc.","first-page":"5","volume-title":"Nonsmooth Optimization","author":"B.T. Polyak","year":"1978","unstructured":"Polyak, B.T.: Subgradient methods: a survey of Soviet research. In: Lemar\u00e9chal, C., Mifflin, R. (eds.) Nonsmooth Optimization. Ser. IIASA Proc., pp.\u00a05\u201329. Pergamon, Elmsford (1978)"},{"key":"9602_CR47","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1007\/BF01584661","volume":"4","author":"A. Pr\u00e9kopa","year":"1973","unstructured":"Pr\u00e9kopa, A.: Contributions to the theory of stochastic programming. Math. Program. 4, 202\u2013221 (1973)","journal-title":"Math. Program."},{"key":"9602_CR48","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0167-6377(99)00063-2","volume":"26","author":"H.D. Sherali","year":"2000","unstructured":"Sherali, H.D., Choi, G., Tubcbilek, C.H.: A variable target value method for nondifferentiable optimization. Oper. Res. Lett. 26, 1\u20138 (2000)","journal-title":"Oper. Res. Lett."},{"key":"9602_CR49","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-82118-9","volume-title":"Minimization Methods for Non-differentiable Functions","author":"N.Z. Shor","year":"1985","unstructured":"Shor, N.Z.: Minimization Methods for Non-differentiable Functions. Springer, Berlin (1985)"},{"key":"9602_CR50","unstructured":"van den Berg, E., Schmidt, M., Friedlander, M.P., Murphy, K.: Group sparsity via linear-time projection. Tech. rep. TR-2008-09, University of British Columbia (2008)"},{"key":"9602_CR51","doi-asserted-by":"crossref","first-page":"2479","DOI":"10.1109\/TSP.2009.2016892","volume":"57","author":"S.J. Wright","year":"2009","unstructured":"Wright, S.J., Nowak, R.D., Figueiredo, M.A.T.: Sparse reconstruction by seperable approximation. IEEE Trans. Signal Process. 57, 2479\u20132493 (2009)","journal-title":"IEEE Trans. Signal Process."},{"key":"9602_CR52","doi-asserted-by":"crossref","first-page":"616","DOI":"10.1080\/01630563.2010.489248","volume":"31","author":"A.J. Zaslavski","year":"2010","unstructured":"Zaslavski, A.J.: The projected subgradient method for nonsmooth convex optimization in the presence of computational error. Numer. Funct. Anal. Optim. 31, 616\u2013633 (2010)","journal-title":"Numer. Funct. Anal. Optim."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-013-9602-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-013-9602-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-013-9602-3","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\/s10589-013-9602-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,9,20]]},"references-count":52,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2014,3]]}},"alternative-id":["9602"],"URL":"https:\/\/doi.org\/10.1007\/s10589-013-9602-3","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,9,20]]}}}