{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,27]],"date-time":"2026-04-27T15:15:34Z","timestamp":1777302934295,"version":"3.51.4"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2013,5,17]],"date-time":"2013-05-17T00:00:00Z","timestamp":1368748800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2014,8]]},"DOI":"10.1007\/s10107-013-0679-3","type":"journal-article","created":{"date-parts":[[2013,5,16]],"date-time":"2013-05-16T03:26:08Z","timestamp":1368674768000},"page":"77-96","source":"Crossref","is-referenced-by-count":13,"title":["Sobolev seminorm of quadratic functions with applications to derivative-free optimization"],"prefix":"10.1007","volume":"146","author":[{"given":"Zaikun","family":"Zhang","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2013,5,17]]},"reference":[{"key":"679_CR1","volume-title":"Sobolev Spaces. Pure and Applied Mathematics","author":"RA Adams","year":"1975","unstructured":"Adams, R.A.: Sobolev Spaces. Pure and Applied Mathematics. Academic Press, London (1975)"},{"issue":"1","key":"679_CR2","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/s10107-012-0578-z","volume":"134","author":"AS Bandeira","year":"2012","unstructured":"Bandeira, A.S., Scheinberg, K., Vicente, L.N.: Computation of sparse low degree interpolating polynomials and their application to derivative-free optimization. Math. Program. 134(1), 223\u2013257 (2012)","journal-title":"Math. Program."},{"issue":"1","key":"679_CR3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01197708","volume":"17","author":"AJ Booker","year":"1999","unstructured":"Booker, A.J., Dennis, J.E., Frank, P.D., Serafini, D.B., Torczon, V., Trosset, M.W.: A rigorous framework for optimization of expensive functions by surrogates. Struct. Multidiscip. Optim. 17(1), 1\u201313 (1999)","journal-title":"Struct. Multidiscip. Optim."},{"key":"679_CR4","unstructured":"Booker, A.J., Dennis Jr, J.E., Frank, P., Serafini, D.B., Torczon, V., Trosset, M.W.: Optimization using surrogate objectives on a helicopter test example. Prog. Syst. Control Theory 24, 49\u201358 (1998)"},{"key":"679_CR5","doi-asserted-by":"crossref","unstructured":"Booker, A.J., Frank, P., Dennis Jr, J.E., Moore, D.W., Serafini, D.B.: Managing surrogate objectives to optimize helicopter rotor design-further experiments. In: Proceedings of the Seventh AIAA\/USAF\/NASA\/ISSMO Symposium on Multidisciplinary Analysis and Optimization (1998)","DOI":"10.2514\/6.1998-4717"},{"key":"679_CR6","volume-title":"Algorithms for Minimization Without Derivatives","author":"RP Brent","year":"1973","unstructured":"Brent, R.P.: Algorithms for Minimization Without Derivatives. Prentice-Hall, Englewood Cliffs (1973)"},{"issue":"4","key":"679_CR7","doi-asserted-by":"crossref","first-page":"1149","DOI":"10.1137\/S1052623499354096","volume":"10","author":"TD Choi","year":"2000","unstructured":"Choi, T.D., Kelley, C.T.: Superlinear convergence and implicit filtering. SIAM J. Optim. 10(4), 1149\u20131162 (2000)","journal-title":"SIAM J. Optim."},{"key":"679_CR8","doi-asserted-by":"crossref","unstructured":"Conn, A.R., Gould, N.I.M., Toint, Ph.L.: Trust-Region Methods, MPS-SIAM series on optimization, Vol. 1. Society for Industrial Mathematics (2000)","DOI":"10.1137\/1.9780898719857"},{"key":"679_CR9","unstructured":"Conn, A.R., Scheinberg, K., Toint, Ph.L.: On the convergence of derivative-free methods for unconstrained optimization. In: Buhmann, M.D., Iserles, A. (eds.) Approximation Theory and Optimization: Tributes to M. J. D. Powell, pp. 83\u2013108. Cambridge University Press, Cambridge (1997)"},{"key":"679_CR10","doi-asserted-by":"crossref","unstructured":"Conn, A.R., Scheinberg, K., Toint, Ph.L.: Recent progress in unconstrained nonlinear optimization without derivatives. Math. Program. 79, 397\u2013414 (1997)","DOI":"10.1007\/BF02614326"},{"key":"679_CR11","doi-asserted-by":"crossref","unstructured":"Conn, A.R., Scheinberg, K., Toint, Ph.L.: A derivative free optimization algorithm in practice. In: Proceedings of 7th AIAA\/USAF\/NASA\/ISSMO Symposium on Multidisciplinary Analysis and Optimization. St. Louis, MO (1998)","DOI":"10.2514\/6.1998-4718"},{"key":"679_CR12","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898718768","volume-title":"Introduction to Derivative-Free Optimization","author":"AR Conn","year":"2009","unstructured":"Conn, A.R., Scheinberg, K., Vicente, L.N.: Introduction to Derivative-Free Optimization. Society for Industrial and Applied Mathematics, Philadelphia (2009)"},{"key":"679_CR13","doi-asserted-by":"crossref","unstructured":"Conn, A.R., Toint, Ph.L.: An algorithm using quadratic interpolation for unconstrained derivative free optimization. In: Di Pillo, G., Giannessi, F. (eds.) Nonlinear Optimization and Applications, pp. 27\u201347. Kluwer Academic\/Plenum Publishers, New York (1996)","DOI":"10.1007\/978-1-4899-0289-4_3"},{"issue":"2","key":"679_CR14","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/s10589-009-9283-0","volume":"46","author":"AL Cust\u00f3dio","year":"2010","unstructured":"Cust\u00f3dio, A.L., Rocha, H., Vicente, L.N.: Incorporating minimum frobenius norm models in direct search. Comput. Optim. Appl. 46(2), 265\u2013278 (2010)","journal-title":"Comput. Optim. Appl."},{"key":"679_CR15","doi-asserted-by":"crossref","unstructured":"Dennis Jr, J.E., Schnabel, R.B.: Least change secant updates for quasi-newton methods. SIAM Rev. 21(4), 443\u2013459 (1979)","DOI":"10.1137\/1021091"},{"issue":"2","key":"679_CR16","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1016\/j.cam.2007.07.017","volume":"219","author":"MA Diniz-Ehrhardt","year":"2008","unstructured":"Diniz-Ehrhardt, M.A., Mart\u00ednez, J.M., Rayd\u00e1n, M.: A derivative-free nonmonotone line-search technique for unconstrained optimization. J. Comput. Appl. Math. 219(2), 383\u2013397 (2008)","journal-title":"J. Comput. Appl. Math."},{"issue":"2","key":"679_CR17","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s101070100263","volume":"91","author":"ED Dolan","year":"2002","unstructured":"Dolan, E.D., Mor\u00e9, J.J.: Benchmarking optimization software with performance profiles. Math. Program. 91(2), 201\u2013213 (2002)","journal-title":"Math. Program."},{"key":"679_CR18","volume-title":"Partial Differential Equations. Graduate Studies in Mathematics","author":"LC Evans","year":"1998","unstructured":"Evans, L.C.: Partial Differential Equations. Graduate Studies in Mathematics. American Mathematical Society, Providence (1998)"},{"key":"679_CR19","volume-title":"Practical Methods of Optimization","author":"R Fletcher","year":"1987","unstructured":"Fletcher, R.: Practical Methods of Optimization, 2nd edn. Wiley, New York (1987)","edition":"2"},{"issue":"5","key":"679_CR20","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1016\/j.advwatres.2008.01.010","volume":"31","author":"KR Fowler","year":"2008","unstructured":"Fowler, K.R., Reese, J.P., Kees, C.E., Kelley, C.T., Miller, C.T., Audet, C., Booker, A.J., Couture, G., Darwin, R.W.: Comparison of derivative-free optimization methods for groundwater supply and hydraulic capture community problems. Adv. Water Res. 31(5), 743\u2013757 (2008)","journal-title":"Adv. Water Res."},{"key":"679_CR21","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1137\/0805015","volume":"5","author":"P Gilmore","year":"1995","unstructured":"Gilmore, P., Kelley, C.T.: An implicit filtering algorithm for optimization of functions with many local minima. SIAM J. Optim. 5, 269 (1995)","journal-title":"SIAM J. Optim."},{"issue":"4","key":"679_CR22","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1145\/962437.962439","volume":"29","author":"NIM Gould","year":"2003","unstructured":"Gould, N.I.M., Orban, D., Toint, PhL: CUTEr and SifDec: a constrained and unconstrained testing environment, revisited. ACM Trans. Math. Softw. (TOMS) 29(4), 373\u2013394 (2003)","journal-title":"ACM Trans. Math. Softw. (TOMS)"},{"key":"679_CR23","unstructured":"Hemker, T., Fowler, K., Von Stryk, O.: Derivative-free optimization methods for handling fixed costs in optimal groundwater remediation design. In: Proceedings of the CMWR XVI-Computational Methods in Water Resources, pp. 19\u201322 (2006)"},{"key":"679_CR24","doi-asserted-by":"crossref","unstructured":"Kelley, C.: Iterative Methods for Optimization, Frontiers in Applied Mathematics, Vol. 18. Society for Industrial Mathematics (1999)","DOI":"10.1137\/1.9781611970920"},{"key":"679_CR25","unstructured":"Kelley, C.T.: A brief introduction to implicit filtering. North Carolina State University, Raleigh, NC, CRSC, Technical Report CRSC-TR02-28 (2002)"},{"key":"679_CR26","doi-asserted-by":"crossref","unstructured":"Kelley, C.T.: Implicit Filtering. Society for Industrial and Applied Mathematics (2011)","DOI":"10.1137\/1.9781611971903"},{"key":"679_CR27","doi-asserted-by":"crossref","unstructured":"Kolda, T.G., Lewis, R.M., Torczon, V.: Optimization by direct search: new perspectives on some classical and modern methods. SIAM Rev. 45(3), 385\u2013482 (2003)","DOI":"10.1137\/S003614450242889"},{"issue":"1","key":"679_CR28","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/S0377-0427(00)00423-4","volume":"124","author":"RM Lewis","year":"2000","unstructured":"Lewis, R.M., Torczon, V., Trosset, M.W.: Direct search methods: then and now. J. Comput. Appl. Math. 124(1), 191\u2013207 (2000)","journal-title":"J. Comput. Appl. Math."},{"issue":"2","key":"679_CR29","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1007\/s101070100264","volume":"91","author":"M Marazzi","year":"2002","unstructured":"Marazzi, M., Nocedal, J.: Wedge trust region methods for derivative free optimization. Math. Program. 91(2), 289\u2013305 (2002)","journal-title":"Math. Program."},{"key":"679_CR30","unstructured":"Oeuvray, R.: Trust-region methods based on radial basis functions with application to biomedical imaging. Ph.D. thesis, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (2005)"},{"issue":"2","key":"679_CR31","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1080\/02286203.2007.11442407","volume":"27","author":"R Oeuvray","year":"2007","unstructured":"Oeuvray, R., Bierlaire, M.: A new derivative-free algorithm for the medical image registration problem. Int. J. Model. Simul. 27(2), 115\u2013124 (2007)","journal-title":"Int. J. Model. Simul."},{"key":"679_CR32","unstructured":"Oeuvray, R., Bierlaire, M.: BOOSTERS: A derivative-free algorithm based on radial basis functions. Int. J. Model. Simul. 29(1), 26\u201336 (2009)"},{"key":"679_CR33","doi-asserted-by":"crossref","unstructured":"Powell, M.J.D.: A direct search optimization method that models the objective and constraint functions by linear interpolation. In: Gomez, S., Hennart, J.P. (eds.) Advances in Optimization and Numerical Analysis: Proceedings of the Sixth Workshop on Optimization and Numerical Analysis (Oaxaca, Mexico), pp. 51\u201367. Kluwer Academic, Dordrecht (1994)","DOI":"10.1007\/978-94-015-8330-5_4"},{"issue":"1","key":"679_CR34","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1017\/S0962492900002841","volume":"7","author":"MJD Powell","year":"1998","unstructured":"Powell, M.J.D.: Direct search algorithms for optimization calculations. Acta Numerica 7(1), 287\u2013336 (1998)","journal-title":"Acta Numerica"},{"key":"679_CR35","unstructured":"Powell, M.J.D.: UOBYQA: unconstrained optimization by quadratic approximation. Technical Report in DAMTP NA2000\/14, CMS, University of Cambridge (2000)"},{"issue":"3","key":"679_CR36","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1007\/s10107-003-0430-6","volume":"97","author":"MJD Powell","year":"2003","unstructured":"Powell, M.J.D.: On trust region methods for unconstrained minimization without derivatives. Math. Program. 97(3), 605\u2013623 (2003)","journal-title":"Math. Program."},{"key":"679_CR37","first-page":"183","volume":"100","author":"MJD Powell","year":"2004","unstructured":"Powell, M.J.D.: Least frobenius norm updating of quadratic models that satisfy interpolation conditions. Math. Program. 100, 183\u2013215 (2004)","journal-title":"Math. Program."},{"key":"679_CR38","unstructured":"Powell, M.J.D.: The NEWUOA software for unconstrained optimization without derivatives. Technical Report in DAMTP NA2004\/08, CMS, University of Cambridge (2004)"},{"key":"679_CR39","doi-asserted-by":"crossref","unstructured":"Powell, M.J.D.: Developments of NEWUOA for minimization without derivatives. IMA J. Numer. Anal. 649\u2013664 (2008) doi: 10.1093\/imanum\/drm047","DOI":"10.1093\/imanum\/drm047"},{"key":"679_CR40","unstructured":"Powell, M.J.D.: The BOBYQA algorithm for bound constrained optimization without derivatives. Technical Report in DAMTP 2009\/NA06, CMS, University of Cambridge (2009)"},{"key":"679_CR41","doi-asserted-by":"crossref","unstructured":"Powell, M.J.D.: Beyond symmetric Broyden for updating quadratic models in minimization without derivatives. Math. Program. 1\u201326 (2012) doi: 10.1007\/s10107-011-0510-y","DOI":"10.1007\/s10107-011-0510-y"},{"issue":"1","key":"679_CR42","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1145\/321371.321377","volume":"14","author":"G Stewart III","year":"1967","unstructured":"Stewart III, G.: A modification of davidon\u2019s minimization method to accept difference approximations of derivatives. J. ACM (JACM) 14(1), 72\u201383 (1967)","journal-title":"J. ACM (JACM)"},{"issue":"1","key":"679_CR43","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/j.cam.2004.11.029","volume":"181","author":"F Berghen Vanden","year":"2005","unstructured":"Berghen Vanden, F., Bersini, H.: CONDOR, a new parallel, constrained extension of powell\u2019s UOBYQA algorithm: Experimental results and comparison with the DFO algorithm. J. Comput. Appl. Math. 181(1), 157\u2013175 (2005)","journal-title":"J. Comput. Appl. Math."},{"key":"679_CR44","unstructured":"Wild, S.M.: MNH: a derivative-free optimization algorithm using minimal norm Hessians. In: Tenth Copper Mountain Conference on Iterative Methods (2008)"},{"issue":"6","key":"679_CR45","doi-asserted-by":"crossref","first-page":"3197","DOI":"10.1137\/070691814","volume":"30","author":"SM Wild","year":"2008","unstructured":"Wild, S.M., Regis, R.G., Shoemaker, C.A.: ORBIT: optimization by radial basis function interpolation in trust-regions. SIAM J. Sci. Comput. 30(6), 3197\u20133219 (2008)","journal-title":"SIAM J. Sci. Comput."},{"issue":"3","key":"679_CR46","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1093\/imamat\/12.3.339","volume":"12","author":"DH Winfield","year":"1973","unstructured":"Winfield, D.H.: Function minimization by interpolation in a data table. IMA J. Appl. Math. 12(3), 339 (1973)","journal-title":"IMA J. Appl. Math."},{"key":"679_CR47","unstructured":"Wright, M.H.: Direct search methods: Once scorned, now respectable. Pitman Research Notes in Mathematics Series, pp. 191\u2013208 (1996)"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-013-0679-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-013-0679-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-013-0679-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,13]],"date-time":"2019-07-13T17:45:32Z","timestamp":1563039932000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-013-0679-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,5,17]]},"references-count":47,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2014,8]]}},"alternative-id":["679"],"URL":"https:\/\/doi.org\/10.1007\/s10107-013-0679-3","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,5,17]]}}}