{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T07:34:08Z","timestamp":1761896048168},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2015,5,24]],"date-time":"2015-05-24T00:00:00Z","timestamp":1432425600000},"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":[[2016,3]]},"DOI":"10.1007\/s10107-015-0908-z","type":"journal-article","created":{"date-parts":[[2015,5,23]],"date-time":"2015-05-23T03:59:38Z","timestamp":1432353578000},"page":"549-579","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Variable metric random pursuit"],"prefix":"10.1007","volume":"156","author":[{"given":"S. U.","family":"Stich","sequence":"first","affiliation":[]},{"given":"C. L.","family":"M\u00fcller","sequence":"additional","affiliation":[]},{"given":"B.","family":"G\u00e4rtner","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,5,24]]},"reference":[{"key":"908_CR1","first-page":"535","volume":"23","author":"R Adamczak","year":"2010","unstructured":"Adamczak, R., Litvak, A.E., Pajor, A., Tomczak-Jaegermann, N.: Quantitative estimates of the convergence of the empirical covariance matrix in log-concave ensembles. J. AMS 23, 535\u2013561 (2010). doi: 10.1090\/S0894-0347-09-00650-X","journal-title":"J. AMS"},{"key":"908_CR2","doi-asserted-by":"crossref","unstructured":"Armijo, L.: Minimization of functions having Lipschitz continuous first partial derivatives. Pac. J. Math. 16(1), 1\u20133 (1966). http:\/\/projecteuclid.org\/euclid.pjm\/1102995080","DOI":"10.2140\/pjm.1966.16.1"},{"key":"908_CR3","doi-asserted-by":"crossref","unstructured":"Brockhoff, D., Auger, A., Hansen, N., Arnold, D., Hohm, T.: Mirrored Sampling and Sequential Selection for Evolution Strategies. In: Schaefer, R., Cotta, C., Ko\u0142odziej, J., Rudolph, G.(eds.) PPSN XI, LNCS, vol. 6238, pp. 11\u201321. Springer, Berlin, Heidelberg (2011). doi: 10.1007\/978-3-642-15844-5_2","DOI":"10.1007\/978-3-642-15844-5_2"},{"key":"908_CR4","doi-asserted-by":"crossref","unstructured":"Broyden, C.G.: The convergence of a class of double-rank minimization algorithms 1. General considerations. IMA J. Appl. Math. 6(1), 76\u201390 (1970). doi: 10.1093\/imamat\/6.1.76 . http:\/\/imamat.oxfordjournals.org\/content\/6\/1\/76.abstract","DOI":"10.1093\/imamat\/6.1.76"},{"key":"908_CR5","doi-asserted-by":"crossref","unstructured":"Davidon, W.C.: Variable metric method for minimization. SIAM J. Optim. 1(1), 1\u201317 (1991). doi: 10.1137\/0801001 . http:\/\/link.aip.org\/link\/?SJE\/1\/1\/1","DOI":"10.1137\/0801001"},{"key":"908_CR6","doi-asserted-by":"crossref","unstructured":"Fletcher, R.: A new approach to variable metric algorithms. Comput. J. 13(3), 317\u2013322 (1970). doi: 10.1093\/comjnl\/13.3.317 . URL http:\/\/comjnl.oxfordjournals.org\/content\/13\/3\/317.abstract","DOI":"10.1093\/comjnl\/13.3.317"},{"key":"908_CR7","doi-asserted-by":"crossref","unstructured":"Goldfarb, D.: A family of variable-metric methods derived by variational means. Math. Comput. 24(109), 23\u201326 (1970). http:\/\/www.jstor.org\/stable\/2004873","DOI":"10.1090\/S0025-5718-1970-0258249-6"},{"issue":"1","key":"908_CR8","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1137\/0303013","volume":"3","author":"A Goldstein","year":"1965","unstructured":"Goldstein, A.: On steepest descent. J. Soc. Ind. Appl. Math. Ser. A Control 3(1), 147\u2013151 (1965). doi: 10.1137\/0303013","journal-title":"J. Soc. Ind. Appl. Math. Ser. A Control"},{"issue":"2","key":"908_CR9","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1162\/106365601750190398","volume":"9","author":"N Hansen","year":"2001","unstructured":"Hansen, N., Ostermeier, A.: Completely derandomized self-adaption in evolution strategies. Evol. Comput. 9(2), 159\u2013195 (2001)","journal-title":"Evol. Comput."},{"key":"908_CR10","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/BF02927114","volume":"40","author":"R Heijmans","year":"1999","unstructured":"Heijmans, R.: When does the expectation of a ratio equal the ratio of expectations? Stat. Pap. 40, 107\u2013115 (1999)","journal-title":"Stat. Pap."},{"key":"908_CR11","series-title":"Reprint 1990 edn","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511810817","volume-title":"Matrix Analysis","author":"RA Horn","year":"1985","unstructured":"Horn, R.A., Johnson, C.R.: Matrix Analysis. Reprint 1990 edn. Cambridge University Press, Cambridge (1985)"},{"key":"908_CR12","doi-asserted-by":"crossref","unstructured":"Hu, T.C., Klee, V., Larman, D.: Optimization of globally convex functions. SIAM J. Control Optim. 27(5), 1026\u20131047 (1989). doi: 10.1137\/0327055 . http:\/\/link.aip.org\/link\/?SJC\/27\/1026\/1","DOI":"10.1137\/0327055"},{"key":"908_CR13","doi-asserted-by":"crossref","unstructured":"J\u00e4gersk\u00fcpper, J.: Lower bounds for hit-and-run direct search. In: J. Hromkovic, R. Kr\u00e1lovic, M. Nunkesser, P. Widmayer (eds.) Stochastic Algorithms: Foundations and Applications, Lecture Notes in Comput. Sci., vol. 4665, pp. 118\u2013129. Springer, Berlin (2007)","DOI":"10.1007\/978-3-540-74871-7_11"},{"key":"908_CR14","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611971903","volume-title":"Implicit Filtering","author":"CT Kelley","year":"2011","unstructured":"Kelley, C.T.: Implicit Filtering. SIAM, Philadelphia, PA (2011)"},{"issue":"7","key":"908_CR15","doi-asserted-by":"crossref","first-page":"702","DOI":"10.1109\/TCS.1981.1085030","volume":"28","author":"G Kjellstr\u00f6m","year":"1981","unstructured":"Kjellstr\u00f6m, G., Taxen, L.: Stochastic optimization in system design. IEEE Trans. Circuits Syst. 28(7), 702\u2013715 (1981). doi: 10.1109\/TCS.1981.1085030","journal-title":"IEEE Trans. Circuits Syst."},{"issue":"3","key":"908_CR16","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1080\/02331930903100141","volume":"60","author":"D Leventhal","year":"2011","unstructured":"Leventhal, D., Lewis, A.S.: Randomized Hessian estimation and directional search. Optimization 60(3), 329\u2013345 (2011). doi: 10.1080\/02331930903100141","journal-title":"Optimization"},{"key":"908_CR17","doi-asserted-by":"crossref","unstructured":"Marti, K.: Controlled random search procedures for global optimization. In: V. Arkin, A. Shiraev, R. Wets (eds.) Stochastic Optimization, Lecture Notes in Control and Information Sciences, vol. 81, pp. 457\u2013474. Springer, Berlin (1986)","DOI":"10.1007\/BFb0007122"},{"key":"908_CR18","unstructured":"Mathai, A.M., Provost, S.B.: Quadratic forms in random variables: theory and applications. No. 126. In: Statistics: Textbooks and Monographs. New York, Dekker (1992)"},{"key":"908_CR19","doi-asserted-by":"crossref","unstructured":"M\u00fcller, C.L., Sbalzarini, I.F.: Gaussian adaptation revisited\u2014an entropic view on covariance matrix adaptation. In: C. Di Chio et al. (ed.) EvoApplications, no. 6024 in Lecture Notes in Comput. Sci., pp. 432\u2013441. Springer, Berlin (2010)","DOI":"10.1007\/978-3-642-12239-2_45"},{"key":"908_CR20","doi-asserted-by":"crossref","unstructured":"Nelder, J.A., Mead, R.: A simplex method for function minimization. Comput. J. 7(4), 308\u2013313 (1965). doi: 10.1093\/comjnl\/7.4.308 . http:\/\/comjnl.oxfordjournals.org\/content\/7\/4\/308.abstract","DOI":"10.1093\/comjnl\/7.4.308"},{"key":"908_CR21","unstructured":"Nesterov, Y.: Random Gradient-Free Minimization of Convex Functions. Technical report, ECORE (2011)"},{"key":"908_CR22","doi-asserted-by":"crossref","unstructured":"Powell, M.: The newuoa software for unconstrained optimization without derivatives. In: Pillo, G., Roma, M. (eds.) Large-Scale Nonlinear Optimization, Nonconvex Optimization and Its Applications, vol. 83, pp. 255\u2013297. Springer, US (2006). doi: 10.1007\/0-387-30065-1_16","DOI":"10.1007\/0-387-30065-1_16"},{"key":"908_CR23","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-10473-2","volume-title":"Matrix Tricks for Linear Statistical Models: Our Personal Top Twenty","author":"S Puntanen","year":"2011","unstructured":"Puntanen, S., Styan, G.P.H., Isotalo, J.: Matrix Tricks for Linear Statistical Models: Our Personal Top Twenty. Springer, Berlin Heidelberg (2011)"},{"key":"908_CR24","doi-asserted-by":"crossref","unstructured":"Rosenbrock, H.H.: An automatic method for finding the greatest or least value of a function. Comput. J. 3(3), 175\u2013184 (1960). doi: 10.1093\/comjnl\/3.3.175 . http:\/\/comjnl.oxfordjournals.org\/content\/3\/3\/175.abstract","DOI":"10.1093\/comjnl\/3.3.175"},{"issue":"3","key":"908_CR25","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1109\/TAC.1968.1098903","volume":"13","author":"M Schumer","year":"1968","unstructured":"Schumer, M., Steiglitz, K.: Adaptive step size random search. Autom. Control IEEE Trans. 13(3), 270\u2013276 (1968). doi: 10.1109\/TAC.1968.1098903","journal-title":"Autom. Control IEEE Trans."},{"key":"908_CR26","doi-asserted-by":"crossref","unstructured":"Shanno, D.F.: Conditioning of Quasi-Newton methods for function minimization. Math. Comput. 24(111), 647\u2013656 (1970). http:\/\/www.jstor.org\/stable\/2004840","DOI":"10.1090\/S0025-5718-1970-0274029-X"},{"key":"908_CR27","unstructured":"Stich, S.U.: Convex optimization with random pursuit. ETH Zurich (2014). doi: 10.3929\/ethz-a-010377352"},{"key":"908_CR28","doi-asserted-by":"crossref","unstructured":"Stich, S.U., M\u00fcller, C.L.: On spectral invariance of randomized hessian and covariance matrix adaptation schemes. In: Coello, C., Cutello, V., Deb, K., Forrest, S., Nicosia, G., Pavone, M. (eds.) Parallel Problem Solving from Nature - PPSN XII. Lecture Notes in Computer Science, vol. 7491, pp. 448\u2013457. Springer, Berlin Heidelberg (2012)","DOI":"10.1007\/978-3-642-32937-1_45"},{"issue":"2","key":"908_CR29","doi-asserted-by":"crossref","first-page":"1284","DOI":"10.1137\/110853613","volume":"23","author":"SU Stich","year":"2013","unstructured":"Stich, S.U., M\u00fcller, C.L., G\u00e4rtner, B.: Optimization of convex functions with random pursuit. SIAM J. Optim. 23(2), 1284\u20131309 (2013)","journal-title":"SIAM J. Optim."},{"key":"908_CR30","unstructured":"Stich, S.U., M\u00fcller, C.L., G\u00e4rtner, B.: Supporting online material for: variable metric random pursuit. arXiv:1210.5114 (2014)"},{"key":"908_CR31","volume-title":"Lectures on Matrices","author":"JHM Wedderburn","year":"1938","unstructured":"Wedderburn, J.H.M.: Lectures on Matrices. (Colloquium Publications) AMS, New York (1938)"},{"issue":"2","key":"908_CR32","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1137\/1011036","volume":"11","author":"P Wolfe","year":"1969","unstructured":"Wolfe, P.: Convergence conditions for ascent methods. SIAM Rev. 11(2), 226\u2013235 (1969). doi: 10.1137\/1011036","journal-title":"SIAM Rev."},{"issue":"2","key":"908_CR33","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1137\/1013035","volume":"13","author":"P Wolfe","year":"1971","unstructured":"Wolfe, P.: Convergence conditions for ascent methods. II: Some corrections. SIAM Rev. 13(2), 185\u2013188 (1971). doi: 10.1137\/1013035","journal-title":"SIAM Rev."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-015-0908-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-015-0908-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-015-0908-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T10:00:07Z","timestamp":1559124007000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-015-0908-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,5,24]]},"references-count":33,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2016,3]]}},"alternative-id":["908"],"URL":"https:\/\/doi.org\/10.1007\/s10107-015-0908-z","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,5,24]]}}}