A semi-infinite programming based algorithm for finding minimax optimal designs for nonlinear models
Minimax optimal experimental designs are notoriously difficult to study largely because the optimality criterion is not differentiable and there is no effective algorithm for generating them. We apply semi-infinite programming (SIP) to solve minimax design problems for nonlinear models in a systemat...
Uloženo v:
| Vydáno v: | Statistics and computing Ročník 24; číslo 6; s. 1063 - 1080 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Boston
Springer US
01.11.2014
|
| Témata: | |
| ISSN: | 0960-3174, 1573-1375 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | Minimax optimal experimental designs are notoriously difficult to study largely because the optimality criterion is not differentiable and there is no effective algorithm for generating them. We apply semi-infinite programming (SIP) to solve minimax design problems for nonlinear models in a systematic way using a discretization based strategy and solvers from the General Algebraic Modeling System (GAMS). Using popular models from the biological sciences, we show our approach produces minimax optimal designs that coincide with the few theoretical and numerical optimal designs in the literature. We also show our method can be readily modified to find standardized maximin optimal designs and minimax optimal designs for more complicated problems, such as when the ranges of plausible values for the model parameters are dependent and we want to find a design to minimize the maximal inefficiency of estimates for the model parameters. |
|---|---|
| AbstractList | Minimax optimal experimental designs are notoriously difficult to study largely because the optimality criterion is not differentiable and there is no effective algorithm for generating them. We apply semi-infinite programming (SIP) to solve minimax design problems for nonlinear models in a systematic way using a discretization based strategy and solvers from the General Algebraic Modeling System (GAMS). Using popular models from the biological sciences, we show our approach produces minimax optimal designs that coincide with the few theoretical and numerical optimal designs in the literature. We also show our method can be readily modified to find standardized maximin optimal designs and minimax optimal designs for more complicated problems, such as when the ranges of plausible values for the model parameters are dependent and we want to find a design to minimize the maximal inefficiency of estimates for the model parameters. |
| Author | Wong, Weng Kee Duarte, Belmiro P. M. |
| Author_xml | – sequence: 1 givenname: Belmiro P. M. surname: Duarte fullname: Duarte, Belmiro P. M. email: bduarte@isec.pt organization: Department of Chemical and Biological Engineering, ISEC, Polytechnic Institute of Coimbra, GEPSI, CIEPQPF, Department of Chemical Engineering, University of Coimbra – sequence: 2 givenname: Weng Kee surname: Wong fullname: Wong, Weng Kee organization: Department of Biostatistics, Fielding School of Public Health, UCLA |
| BookMark | eNp9kM1OAyEURompiW31AdzxAihwZ6CzbBr_kiZudE2gMCPNDDSAib691Lpy0dVd3O_c3O8s0CzE4BC6ZfSOUSrvM2Occ0IZkK7hlIgLNGetBMJAtjM0p52gBJhsrtAi5z2ljAlo5siucXaTJz70Pvji8CHFIelp8mHARmdnsR6HmHz5mHAfE64xe9zVgJ_0F46HUueIrct-CPk3U38bfXA64SlaN-ZrdNnrMbubv7lE748Pb5tnsn19etmst2QH7aqQtpcSLO-hFc6AayyAAC5aYanW0OpOdJ00Qhu5sp01btUYDrq2NACSUw1LJE93dynmnFyvdr7o4mMoSftRMaqOstRJlqqy1FGWEpVk_8hDqrXS91mGn5hcs2FwSe3jZwq14BnoB6Zmf5U |
| CitedBy_id | crossref_primary_10_3390_pr7110834 crossref_primary_10_1016_j_chemolab_2015_12_014 crossref_primary_10_1007_s11222_017_9741_y crossref_primary_10_1007_s11222_021_10046_2 crossref_primary_10_1080_01621459_2020_1862670 crossref_primary_10_1177_0962280217709817 crossref_primary_10_1007_s00362_015_0688_9 crossref_primary_10_1007_s00362_017_0887_7 crossref_primary_10_1007_s00362_025_01725_7 crossref_primary_10_1016_j_ces_2024_120566 crossref_primary_10_1080_10618600_2019_1601097 crossref_primary_10_1002_pst_2388 crossref_primary_10_1002_sim_6882 crossref_primary_10_1016_j_csda_2017_09_008 crossref_primary_10_1007_s11222_021_10020_y crossref_primary_10_1007_s11222_024_10465_x crossref_primary_10_1016_j_jmva_2014_11_006 crossref_primary_10_1109_TMI_2016_2574240 crossref_primary_10_1016_j_measurement_2021_110286 crossref_primary_10_1002_cjs_11499 crossref_primary_10_1016_j_jspi_2023_06_005 |
| Cites_doi | 10.1093/oso/9780199296590.001.0001 10.1137/S1052623402406777 10.1111/j.2517-6161.1993.tb01946.x 10.1137/1035089 10.1111/1467-9868.00056 10.1016/0378-3758(89)90004-9 10.1080/0094965031000115402 10.1007/BF00934096 10.1007/978-3-7908-2693-7_5 10.1080/00401706.1974.10489212 10.1080/00224065.2004.11980273 10.1007/0-387-23667-8_2 10.1007/978-1-4757-2868-2 10.1093/biomet/79.3.611 10.1137/0132021 10.4319/lo.1983.28.1.0185 10.6339/JDS.2005.03(2).190 10.1080/01621459.2012.656035 10.1002/9780470746912 10.1016/S0378-3758(00)00137-3 10.1080/00401706.1982.10487708 10.1016/S0378-3758(96)00131-0 10.2307/2529262 10.1080/10543406.2010.489979 10.1007/s10898-008-9321-y 10.1023/B:ANOR.0000004764.76984.30 10.1080/08982112.2011.576203 10.1016/j.spl.2008.01.059 10.1111/j.2517-6161.1972.tb00896.x 10.1080/00401706.1980.10486161 10.1080/00401706.1985.10488048 10.1016/S0167-7152(99)00033-4 10.1016/S0377-2217(01)00307-1 10.1214/ss/1177009939 10.1111/j.0006-341X.2000.01263.x 10.2307/2532705 10.1214/009053606000001307 10.1080/01621459.1971.10482261 10.1016/j.jspi.2010.11.031 10.1007/978-94-009-5912-5 10.1007/BF02591747 10.1023/A:1014878317736 10.1016/0378-3758(94)00042-T 10.1007/BF02296152 |
| ContentType | Journal Article |
| Copyright | Springer Science+Business Media New York 2013 |
| Copyright_xml | – notice: Springer Science+Business Media New York 2013 |
| DBID | AAYXX CITATION |
| DOI | 10.1007/s11222-013-9420-6 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Statistics Mathematics Computer Science |
| EISSN | 1573-1375 |
| EndPage | 1080 |
| ExternalDocumentID | 10_1007_s11222_013_9420_6 |
| GroupedDBID | -52 -5D -5G -BR -EM -Y2 -~C .86 .DC .VR 06D 0R~ 0VY 123 199 1N0 1SB 2.D 203 28- 29Q 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5QI 5VS 67Z 6NX 78A 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABLJU ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFGCZ AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BAPOH BBWZM BDATZ BGNMA BSONS CAG COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 EBLON EBS EIOEI EJD ESBYG F5P FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS H13 HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV KOW LAK LLZTM M4Y MA- N2Q NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM OVD P19 P2P P9R PF0 PT4 PT5 QOK QOS R4E R89 R9I RHV RIG RNI RNS ROL RPX RSV RZC RZE RZK S16 S1Z S26 S27 S28 S3B SAP SCJ SCLPG SDD SDH SDM SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TEORI TN5 TSG TSK TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z45 Z7R Z7U Z7W Z7X Z7Y Z81 Z83 Z87 Z88 Z8O Z8R Z8U Z8W Z91 Z92 ZMTXR ZWQNP ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG ADKFA AEZWR AFDZB AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP ATHPR AYFIA CITATION |
| ID | FETCH-LOGICAL-c358t-5f773d2f356eb3e4d33632656d0aa35a96997b6ab78d9dbe84b23a157b33720a3 |
| IEDL.DBID | RSV |
| ISICitedReferencesCount | 23 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000341440800011&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0960-3174 |
| IngestDate | Sat Nov 29 03:32:41 EST 2025 Tue Nov 18 21:37:28 EST 2025 Fri Feb 21 02:34:26 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 6 |
| Keywords | Fisher Information Matrix General equivalence theorem Power logistic model Semi-infinite programming Minmax problem Continuous design |
| Language | English |
| License | http://www.springer.com/tdm |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c358t-5f773d2f356eb3e4d33632656d0aa35a96997b6ab78d9dbe84b23a157b33720a3 |
| PageCount | 18 |
| ParticipantIDs | crossref_citationtrail_10_1007_s11222_013_9420_6 crossref_primary_10_1007_s11222_013_9420_6 springer_journals_10_1007_s11222_013_9420_6 |
| PublicationCentury | 2000 |
| PublicationDate | 2014-11-01 |
| PublicationDateYYYYMMDD | 2014-11-01 |
| PublicationDate_xml | – month: 11 year: 2014 text: 2014-11-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | Boston |
| PublicationPlace_xml | – name: Boston |
| PublicationTitle | Statistics and computing |
| PublicationTitleAbbrev | Stat Comput |
| PublicationYear | 2014 |
| Publisher | Springer US |
| Publisher_xml | – name: Springer US |
| References | DetteH.NeugebauerH.-M.Bayesian D-optimal designs for exponential regression modelsJ. Stat. Plan. Inference19976033134910.1016/S0378-3758(96)00131-00900.624081456635 LiW.K.W.Consideration of errors in estimating kinetic parameters based on Michaelis-Menten formalism in microbial ecologyLimnol. Oceanogr.19832818519010.4319/lo.1983.28.1.0185 SilveyS.D.Optimal Design1980LondonChapman & Hall10.1007/978-94-009-5912-50468.62070 HamiltonD.C.WattsD.G.A quadratic design criterion for precise estimation in nonlinear regression modelsTechnometrics19852724125010.1080/00401706.1985.104880480598.62083797562 ChenR.B.WongW.K.LiK.Y.Optimal minimax designs over a prespecified interval in a heteroscedastic polynomial modelStat. Probab. Lett.200878131914192110.1016/j.spl.2008.01.0591147.623562528561 MurtyV.N.Minimax designsJ. Am. Stat. Assoc.19716631932010.1080/01621459.1971.104822610216.48201 ChalonerK.LarntzK.Optimal Bayesian design applied to logistic regression experimentsJ. Stat. Plan. Inference19895919120810.1016/0378-3758(89)90004-9985457 GalilZ.KieferJ.Time- and space-saving computer methods, related to Mitchell’s DETMAX for finding D-optimum designsTechnometrics19802230131310.1080/00401706.1980.104861610459.62060585633 KingJ.WongW.K.Minimax D-optimal designs for logistic modelBiometrics2000561263126710.1111/j.0006-341X.2000.01263.x1060.625451816369 MüllerC.H.Maximin efficient designs for estimating nonlinear aspects in linear modelsJ. Stat. Plan. Inference19954411713210.1016/0378-3758(94)00042-T0812.62081 AtkinsonA.C.DonevA.N.TobiasR.D.Optimum Experimental Designs, with SAS2007New YorkOxford University Press1183.62129 SitterR.R.Robust designs for binary dataBiometrics1992481145115510.2307/25327051212858 FedorovV.V.Convex design theoryMath. Oper.forsch. Stat., Ser. Stat.1980114034130471.62075 ChalonerK.VerdinelliI.Bayesian experimental design: a reviewStat. Sci.19951027330410.1214/ss/11770099390955.626171390519 MolchanovI.ZuyevS.Steepest descent algorithm in a space of measuresStat. Comput.20021211512310.1023/A:10148783177361897510 WongW.K.A unified approach to the construction of minimax designsBiometrika19927961162010.1093/biomet/79.3.6110762.620191187611 RoysetJ.PolakE.Der KiureghianA.Adaptive approximations and exact penalization for the solution of generalized semi-infinite min-max problemsSIAM J. Optim.200314113410.1137/S10526234024067771042.490332005934 TsoukalasA.RustemB.PistikopoulosE.N.A global optimization algorithm for generalized semi-infinite, continuous minimax with coupled constraints and bi-level problemsJ. Glob. Optim.20092423525010.1007/s10898-008-9321-y2506674 Heredia-LangnerA.MontgomeryD.C.CarlyleW.M.BorrorC.M.Model-robust optimal designs: a genetic algorithm approachJ. Qual. Technol.200436263279 SagnolG.Computing optimal designs of multiresponse experiments reduces to second-order cone programmingJ. Stat. Plan. Inference201114151684170810.1016/j.jspi.2010.11.0311207.621562763200 WongW.K.CookR.D.Heteroscedastic G-optimal designsJ. R. Stat. Soc. B1993558718800794.620431229885 Chen, R.B., Chang, S.P., Wang, W., Wong, W.K.: Optimal minimax designs via particle swarm optimization methods. Preprints of the Isaac Newton Institute (2013). http://www.newton.ac.uk/preprints/NI13039.pdf CookR.D.NachtsheimC.J.Model robust, linear-optimal designsTechnometrics198224495410.1080/00401706.1982.104877080483.62063653111 PrenticeR.L.A generalization of the probit and logit methods for dose response curvesBiometrics19763276176810.2307/2529262 Fandom NoubiapR.SeidelW.A minimax algorithm for constructing optimal symmetrical balanced designs for a logistic regression modelJ. Stat. Plan. Inference20009115116810.1016/S0378-3758(00)00137-30958.62065 RustemB.HoweM.Algorithms for Worst-Case Design and Applications to Risk Management2002PrincetonPrinceton University Press1140.90013 DetteH.WongW.K.E-optimal designs for the Michaelis-Menten modelStat. Probab. Lett.19994440540810.1016/S0167-7152(99)00033-40940.620661715246 HillW.J.HunterW.G.Design of experiments for subsets of parametersTechnometrics19741642543410.1080/00401706.1974.104892120311.62045359200 UgrayZ.LasdonL.PlummerJ.GloverF.KellyJ.MartíR.A multistart scatter search heuristic for smooth NLP and MINLP problemsMetaheuristic Optimization via Memory and Evolution2005BerlinSpringer255110.1007/0-387-23667-8_2 PappD.Optimal designs for rational function regressionJ. Am. Stat. Assoc.201210740041110.1080/01621459.2012.6560351261.620722949369 BlankenshipJ.W.FalkJ.E.Infinitely constrained optimization problemsJ. Optim. Theory Appl.197619226128110.1007/BF009340960307.90071421675 PázmanA.Foundations of Optimum Experimental Design1986New YorkReidel0588.62117 JohnsonR.T.MontgomeryD.C.JonesB.A.An expository paper on optimal designQual. Eng.20112328730110.1080/08982112.2011.576203 Brooke, A., Kendrick, D., Meeraus, A., Raman, R.: GAMS—a users guide. GAMS Development Corporation, Washington (1998) GribikP.R.KortanekK.O.Equivalence theorems and cutting plane algorithms for a class of experimental design problemsSIAM J. Appl. Math.19773223225910.1137/01320210356.62060433749 MitchellT.J.An algorithm for the construction of D-optimal experimental designsTechnometrics1974162032100297.62055386181 BiedermanS.DetteH.PepelyshevA.Di BucchianicoA.LäuterH.WynnH.P.Maximin optimal designs for a compartmental modelmODa 7—Advances in Model-Oriented Design and Analysis2004HeidelbergPhysica-Verlag414910.1007/978-3-7908-2693-7_5 O’BrienT.E,Designing for parameter subsets in Gaussian nonlinear regression modelsJ. Data Sci.20053179197 HettichR.KortanekK.O.Semi-infinite programming: theory, methods and applicationsSIAM Rev.19933538042910.1137/10350890784.900901234637 BogackaB.PatanM.JohnsonP.J.YoudinK.AtkinsonA.C.Optimum design of experiments for enzyme inhibition kinetic modelsJ. Biopharm. Stat.201121355557210.1080/10543406.2010.489979 DetteH.SahmM.Minimax optimal designs in nonlinear regression modelsStat. Sin.19988124912640916.620531666257 SteinO.StillG.On generalized semi-infinite optimization and bilevel optimizationEur. J. Oper. Res.2002142344446210.1016/S0377-2217(01)00307-10596.650041922367 BraessD.DetteH.On the number of support points of maximin and Bayesian optimal designsAnn. Stat.200735277279210.1214/0090536060000013071117.620742336868 KingJ.WongW.K.Optimal designs for the power logistic modelJ. Stat. Comput. Simul.20047477979110.1080/00949650310001154021060.620832083103 Zhang, Y.: Bayesian D-optimal design for generalized linear models. PhD thesis, Virginia Polytechnic Institute and State University, Blacksburg (2006) FedorovV.V.Theory of Optimal Experiments1972San DiegoAcademic Press DetteH.Designing experiments with respect to “standardized” optimality criteriaJ. R. Stat. Soc. B1997599711010.1111/1467-9868.000560884.620811436556 DrudA.CONOPT: a GRG code for large sparse dynamic nonlinear optimization problemsMath. Program.19853115319110.1007/BF025917470557.90088777289 WynnH.P.Results in the theory and construction of D-optimum experimental designsJ. R. Stat. Soc. B1972341331470248.62033350987 ŽakovićS.RustemB.Semi-infinite programming and applications to minimax problemsAnn. Oper. Res.20031241–4811101074.905542035972 TorsneyB.López-FidalgoJ.KitsosC.P.MüllerW.G.MV-optimization in simple linear regressionmODa 4—Advances in Model-Oriented Data Analysis19957176 ReemtsenR.RückmanJ.J.Semi-Infinite Programming1998DordrechtKluwer Academic10.1007/978-1-4757-2868-20890.00054 BergerM.P.F.KingJ.WongW.K.Minimax D-optimal designs for item response theory modelsPsychometrika200065337739010.1007/BF022961521291.621941792702 Kuczewski, B.: Computational aspects of discrimination between models of dynamic systems. PhD thesis, University of Zielona, Góra, Zielona Góra, Poland (2006) BergerM.P.F.WongW.K.An Introduction to Optimal Designs for Social and Biomedical Research2009New YorkWiley10.1002/97804707469121182.62154 A.C. Atkinson (9420_CR1) 2007 S. Žaković (9420_CR54) 2003; 124 9420_CR55 9420_CR12 J.W. Blankenship (9420_CR5) 1976; 19 W.K.W. Li (9420_CR32) 1983; 28 R. Reemtsen (9420_CR41) 1998 9420_CR8 H. Dette (9420_CR17) 1999; 44 G. Sagnol (9420_CR44) 2011; 141 R.L. Prentice (9420_CR40) 1976; 32 S. Biederman (9420_CR4) 2004 W.J. Hill (9420_CR27) 1974; 16 M.P.F. Berger (9420_CR2) 2009 V.N. Murty (9420_CR36) 1971; 66 A. Drud (9420_CR18) 1985; 31 V.V. Fedorov (9420_CR21) 1980; 11 H.P. Wynn (9420_CR53) 1972; 34 P.R. Gribik (9420_CR23) 1977; 32 K. Chaloner (9420_CR10) 1995; 10 K. Chaloner (9420_CR9) 1989; 59 H. Dette (9420_CR15) 1997; 60 H. Dette (9420_CR16) 1998; 8 A. Pázman (9420_CR39) 1986 R. Fandom Noubiap (9420_CR19) 2000; 91 J. Royset (9420_CR42) 2003; 14 W.K. Wong (9420_CR51) 1992; 79 D. Braess (9420_CR7) 2007; 35 Z. Ugray (9420_CR50) 2005 O. Stein (9420_CR47) 2002; 142 J. King (9420_CR29) 2000; 56 R.R. Sitter (9420_CR46) 1992; 48 V.V. Fedorov (9420_CR20) 1972 A. Heredia-Langner (9420_CR25) 2004; 36 9420_CR31 W.K. Wong (9420_CR52) 1993; 55 J. King (9420_CR30) 2004; 74 B. Rustem (9420_CR43) 2002 R.D. Cook (9420_CR13) 1982; 24 H. Dette (9420_CR14) 1997; 59 A. Tsoukalas (9420_CR49) 2009; 24 T.J. Mitchell (9420_CR33) 1974; 16 B. Torsney (9420_CR48) 1995 B. Bogacka (9420_CR6) 2011; 21 S.D. Silvey (9420_CR45) 1980 T.E, O’Brien (9420_CR37) 2005; 3 R.T. Johnson (9420_CR28) 2011; 23 Z. Galil (9420_CR22) 1980; 22 D. Papp (9420_CR38) 2012; 107 I. Molchanov (9420_CR34) 2002; 12 R.B. Chen (9420_CR11) 2008; 78 D.C. Hamilton (9420_CR24) 1985; 27 C.H. Müller (9420_CR35) 1995; 44 R. Hettich (9420_CR26) 1993; 35 M.P.F. Berger (9420_CR3) 2000; 65 |
| References_xml | – reference: SteinO.StillG.On generalized semi-infinite optimization and bilevel optimizationEur. J. Oper. Res.2002142344446210.1016/S0377-2217(01)00307-10596.650041922367 – reference: WynnH.P.Results in the theory and construction of D-optimum experimental designsJ. R. Stat. Soc. B1972341331470248.62033350987 – reference: TorsneyB.López-FidalgoJ.KitsosC.P.MüllerW.G.MV-optimization in simple linear regressionmODa 4—Advances in Model-Oriented Data Analysis19957176 – reference: FedorovV.V.Theory of Optimal Experiments1972San DiegoAcademic Press – reference: PappD.Optimal designs for rational function regressionJ. Am. Stat. Assoc.201210740041110.1080/01621459.2012.6560351261.620722949369 – reference: ŽakovićS.RustemB.Semi-infinite programming and applications to minimax problemsAnn. Oper. Res.20031241–4811101074.905542035972 – reference: PázmanA.Foundations of Optimum Experimental Design1986New YorkReidel0588.62117 – reference: Zhang, Y.: Bayesian D-optimal design for generalized linear models. PhD thesis, Virginia Polytechnic Institute and State University, Blacksburg (2006) – reference: RoysetJ.PolakE.Der KiureghianA.Adaptive approximations and exact penalization for the solution of generalized semi-infinite min-max problemsSIAM J. Optim.200314113410.1137/S10526234024067771042.490332005934 – reference: BergerM.P.F.KingJ.WongW.K.Minimax D-optimal designs for item response theory modelsPsychometrika200065337739010.1007/BF022961521291.621941792702 – reference: PrenticeR.L.A generalization of the probit and logit methods for dose response curvesBiometrics19763276176810.2307/2529262 – reference: UgrayZ.LasdonL.PlummerJ.GloverF.KellyJ.MartíR.A multistart scatter search heuristic for smooth NLP and MINLP problemsMetaheuristic Optimization via Memory and Evolution2005BerlinSpringer255110.1007/0-387-23667-8_2 – reference: HillW.J.HunterW.G.Design of experiments for subsets of parametersTechnometrics19741642543410.1080/00401706.1974.104892120311.62045359200 – reference: SagnolG.Computing optimal designs of multiresponse experiments reduces to second-order cone programmingJ. Stat. Plan. Inference201114151684170810.1016/j.jspi.2010.11.0311207.621562763200 – reference: CookR.D.NachtsheimC.J.Model robust, linear-optimal designsTechnometrics198224495410.1080/00401706.1982.104877080483.62063653111 – reference: KingJ.WongW.K.Minimax D-optimal designs for logistic modelBiometrics2000561263126710.1111/j.0006-341X.2000.01263.x1060.625451816369 – reference: DetteH.Designing experiments with respect to “standardized” optimality criteriaJ. R. Stat. Soc. B1997599711010.1111/1467-9868.000560884.620811436556 – reference: Heredia-LangnerA.MontgomeryD.C.CarlyleW.M.BorrorC.M.Model-robust optimal designs: a genetic algorithm approachJ. Qual. Technol.200436263279 – reference: MitchellT.J.An algorithm for the construction of D-optimal experimental designsTechnometrics1974162032100297.62055386181 – reference: O’BrienT.E,Designing for parameter subsets in Gaussian nonlinear regression modelsJ. Data Sci.20053179197 – reference: BogackaB.PatanM.JohnsonP.J.YoudinK.AtkinsonA.C.Optimum design of experiments for enzyme inhibition kinetic modelsJ. Biopharm. Stat.201121355557210.1080/10543406.2010.489979 – reference: MüllerC.H.Maximin efficient designs for estimating nonlinear aspects in linear modelsJ. Stat. Plan. Inference19954411713210.1016/0378-3758(94)00042-T0812.62081 – reference: ReemtsenR.RückmanJ.J.Semi-Infinite Programming1998DordrechtKluwer Academic10.1007/978-1-4757-2868-20890.00054 – reference: TsoukalasA.RustemB.PistikopoulosE.N.A global optimization algorithm for generalized semi-infinite, continuous minimax with coupled constraints and bi-level problemsJ. Glob. Optim.20092423525010.1007/s10898-008-9321-y2506674 – reference: BlankenshipJ.W.FalkJ.E.Infinitely constrained optimization problemsJ. Optim. Theory Appl.197619226128110.1007/BF009340960307.90071421675 – reference: Fandom NoubiapR.SeidelW.A minimax algorithm for constructing optimal symmetrical balanced designs for a logistic regression modelJ. Stat. Plan. Inference20009115116810.1016/S0378-3758(00)00137-30958.62065 – reference: WongW.K.A unified approach to the construction of minimax designsBiometrika19927961162010.1093/biomet/79.3.6110762.620191187611 – reference: MolchanovI.ZuyevS.Steepest descent algorithm in a space of measuresStat. Comput.20021211512310.1023/A:10148783177361897510 – reference: DetteH.SahmM.Minimax optimal designs in nonlinear regression modelsStat. Sin.19988124912640916.620531666257 – reference: HettichR.KortanekK.O.Semi-infinite programming: theory, methods and applicationsSIAM Rev.19933538042910.1137/10350890784.900901234637 – reference: ChenR.B.WongW.K.LiK.Y.Optimal minimax designs over a prespecified interval in a heteroscedastic polynomial modelStat. Probab. Lett.200878131914192110.1016/j.spl.2008.01.0591147.623562528561 – reference: LiW.K.W.Consideration of errors in estimating kinetic parameters based on Michaelis-Menten formalism in microbial ecologyLimnol. Oceanogr.19832818519010.4319/lo.1983.28.1.0185 – reference: AtkinsonA.C.DonevA.N.TobiasR.D.Optimum Experimental Designs, with SAS2007New YorkOxford University Press1183.62129 – reference: WongW.K.CookR.D.Heteroscedastic G-optimal designsJ. R. Stat. Soc. B1993558718800794.620431229885 – reference: KingJ.WongW.K.Optimal designs for the power logistic modelJ. Stat. Comput. Simul.20047477979110.1080/00949650310001154021060.620832083103 – reference: FedorovV.V.Convex design theoryMath. Oper.forsch. Stat., Ser. Stat.1980114034130471.62075 – reference: BergerM.P.F.WongW.K.An Introduction to Optimal Designs for Social and Biomedical Research2009New YorkWiley10.1002/97804707469121182.62154 – reference: SitterR.R.Robust designs for binary dataBiometrics1992481145115510.2307/25327051212858 – reference: DetteH.WongW.K.E-optimal designs for the Michaelis-Menten modelStat. Probab. Lett.19994440540810.1016/S0167-7152(99)00033-40940.620661715246 – reference: HamiltonD.C.WattsD.G.A quadratic design criterion for precise estimation in nonlinear regression modelsTechnometrics19852724125010.1080/00401706.1985.104880480598.62083797562 – reference: Brooke, A., Kendrick, D., Meeraus, A., Raman, R.: GAMS—a users guide. GAMS Development Corporation, Washington (1998) – reference: ChalonerK.VerdinelliI.Bayesian experimental design: a reviewStat. Sci.19951027330410.1214/ss/11770099390955.626171390519 – reference: BiedermanS.DetteH.PepelyshevA.Di BucchianicoA.LäuterH.WynnH.P.Maximin optimal designs for a compartmental modelmODa 7—Advances in Model-Oriented Design and Analysis2004HeidelbergPhysica-Verlag414910.1007/978-3-7908-2693-7_5 – reference: ChalonerK.LarntzK.Optimal Bayesian design applied to logistic regression experimentsJ. Stat. Plan. Inference19895919120810.1016/0378-3758(89)90004-9985457 – reference: SilveyS.D.Optimal Design1980LondonChapman & Hall10.1007/978-94-009-5912-50468.62070 – reference: RustemB.HoweM.Algorithms for Worst-Case Design and Applications to Risk Management2002PrincetonPrinceton University Press1140.90013 – reference: GalilZ.KieferJ.Time- and space-saving computer methods, related to Mitchell’s DETMAX for finding D-optimum designsTechnometrics19802230131310.1080/00401706.1980.104861610459.62060585633 – reference: DetteH.NeugebauerH.-M.Bayesian D-optimal designs for exponential regression modelsJ. Stat. Plan. Inference19976033134910.1016/S0378-3758(96)00131-00900.624081456635 – reference: DrudA.CONOPT: a GRG code for large sparse dynamic nonlinear optimization problemsMath. Program.19853115319110.1007/BF025917470557.90088777289 – reference: Chen, R.B., Chang, S.P., Wang, W., Wong, W.K.: Optimal minimax designs via particle swarm optimization methods. Preprints of the Isaac Newton Institute (2013). http://www.newton.ac.uk/preprints/NI13039.pdf – reference: BraessD.DetteH.On the number of support points of maximin and Bayesian optimal designsAnn. Stat.200735277279210.1214/0090536060000013071117.620742336868 – reference: MurtyV.N.Minimax designsJ. Am. Stat. Assoc.19716631932010.1080/01621459.1971.104822610216.48201 – reference: Kuczewski, B.: Computational aspects of discrimination between models of dynamic systems. PhD thesis, University of Zielona, Góra, Zielona Góra, Poland (2006) – reference: GribikP.R.KortanekK.O.Equivalence theorems and cutting plane algorithms for a class of experimental design problemsSIAM J. Appl. Math.19773223225910.1137/01320210356.62060433749 – reference: JohnsonR.T.MontgomeryD.C.JonesB.A.An expository paper on optimal designQual. Eng.20112328730110.1080/08982112.2011.576203 – start-page: 71 volume-title: mODa 4—Advances in Model-Oriented Data Analysis year: 1995 ident: 9420_CR48 – volume-title: Optimum Experimental Designs, with SAS year: 2007 ident: 9420_CR1 doi: 10.1093/oso/9780199296590.001.0001 – volume: 14 start-page: 1 issue: 1 year: 2003 ident: 9420_CR42 publication-title: SIAM J. Optim. doi: 10.1137/S1052623402406777 – volume: 55 start-page: 871 year: 1993 ident: 9420_CR52 publication-title: J. R. Stat. Soc. B doi: 10.1111/j.2517-6161.1993.tb01946.x – volume: 35 start-page: 380 year: 1993 ident: 9420_CR26 publication-title: SIAM Rev. doi: 10.1137/1035089 – volume: 59 start-page: 97 year: 1997 ident: 9420_CR14 publication-title: J. R. Stat. Soc. B doi: 10.1111/1467-9868.00056 – volume: 59 start-page: 191 year: 1989 ident: 9420_CR9 publication-title: J. Stat. Plan. Inference doi: 10.1016/0378-3758(89)90004-9 – volume: 74 start-page: 779 year: 2004 ident: 9420_CR30 publication-title: J. Stat. Comput. Simul. doi: 10.1080/0094965031000115402 – volume: 19 start-page: 261 issue: 2 year: 1976 ident: 9420_CR5 publication-title: J. Optim. Theory Appl. doi: 10.1007/BF00934096 – volume: 8 start-page: 1249 year: 1998 ident: 9420_CR16 publication-title: Stat. Sin. – start-page: 41 volume-title: mODa 7—Advances in Model-Oriented Design and Analysis year: 2004 ident: 9420_CR4 doi: 10.1007/978-3-7908-2693-7_5 – volume: 16 start-page: 425 year: 1974 ident: 9420_CR27 publication-title: Technometrics doi: 10.1080/00401706.1974.10489212 – volume: 36 start-page: 263 year: 2004 ident: 9420_CR25 publication-title: J. Qual. Technol. doi: 10.1080/00224065.2004.11980273 – start-page: 25 volume-title: Metaheuristic Optimization via Memory and Evolution year: 2005 ident: 9420_CR50 doi: 10.1007/0-387-23667-8_2 – volume-title: Semi-Infinite Programming year: 1998 ident: 9420_CR41 doi: 10.1007/978-1-4757-2868-2 – volume: 79 start-page: 611 year: 1992 ident: 9420_CR51 publication-title: Biometrika doi: 10.1093/biomet/79.3.611 – volume: 32 start-page: 232 year: 1977 ident: 9420_CR23 publication-title: SIAM J. Appl. Math. doi: 10.1137/0132021 – volume: 28 start-page: 185 year: 1983 ident: 9420_CR32 publication-title: Limnol. Oceanogr. doi: 10.4319/lo.1983.28.1.0185 – volume: 3 start-page: 179 year: 2005 ident: 9420_CR37 publication-title: J. Data Sci. doi: 10.6339/JDS.2005.03(2).190 – volume: 107 start-page: 400 year: 2012 ident: 9420_CR38 publication-title: J. Am. Stat. Assoc. doi: 10.1080/01621459.2012.656035 – volume-title: An Introduction to Optimal Designs for Social and Biomedical Research year: 2009 ident: 9420_CR2 doi: 10.1002/9780470746912 – volume: 91 start-page: 151 year: 2000 ident: 9420_CR19 publication-title: J. Stat. Plan. Inference doi: 10.1016/S0378-3758(00)00137-3 – volume: 24 start-page: 49 year: 1982 ident: 9420_CR13 publication-title: Technometrics doi: 10.1080/00401706.1982.10487708 – volume-title: Foundations of Optimum Experimental Design year: 1986 ident: 9420_CR39 – volume: 60 start-page: 331 year: 1997 ident: 9420_CR15 publication-title: J. Stat. Plan. Inference doi: 10.1016/S0378-3758(96)00131-0 – volume: 32 start-page: 761 year: 1976 ident: 9420_CR40 publication-title: Biometrics doi: 10.2307/2529262 – volume: 21 start-page: 555 issue: 3 year: 2011 ident: 9420_CR6 publication-title: J. Biopharm. Stat. doi: 10.1080/10543406.2010.489979 – volume: 24 start-page: 235 year: 2009 ident: 9420_CR49 publication-title: J. Glob. Optim. doi: 10.1007/s10898-008-9321-y – ident: 9420_CR12 – volume: 124 start-page: 81 issue: 1–4 year: 2003 ident: 9420_CR54 publication-title: Ann. Oper. Res. doi: 10.1023/B:ANOR.0000004764.76984.30 – volume: 23 start-page: 287 year: 2011 ident: 9420_CR28 publication-title: Qual. Eng. doi: 10.1080/08982112.2011.576203 – volume: 78 start-page: 1914 issue: 13 year: 2008 ident: 9420_CR11 publication-title: Stat. Probab. Lett. doi: 10.1016/j.spl.2008.01.059 – volume: 34 start-page: 133 year: 1972 ident: 9420_CR53 publication-title: J. R. Stat. Soc. B doi: 10.1111/j.2517-6161.1972.tb00896.x – volume: 22 start-page: 301 year: 1980 ident: 9420_CR22 publication-title: Technometrics doi: 10.1080/00401706.1980.10486161 – volume: 27 start-page: 241 year: 1985 ident: 9420_CR24 publication-title: Technometrics doi: 10.1080/00401706.1985.10488048 – volume: 44 start-page: 405 year: 1999 ident: 9420_CR17 publication-title: Stat. Probab. Lett. doi: 10.1016/S0167-7152(99)00033-4 – volume-title: Theory of Optimal Experiments year: 1972 ident: 9420_CR20 – ident: 9420_CR8 – volume: 142 start-page: 444 issue: 3 year: 2002 ident: 9420_CR47 publication-title: Eur. J. Oper. Res. doi: 10.1016/S0377-2217(01)00307-1 – ident: 9420_CR55 – volume: 10 start-page: 273 year: 1995 ident: 9420_CR10 publication-title: Stat. Sci. doi: 10.1214/ss/1177009939 – volume: 56 start-page: 1263 year: 2000 ident: 9420_CR29 publication-title: Biometrics doi: 10.1111/j.0006-341X.2000.01263.x – volume: 48 start-page: 1145 year: 1992 ident: 9420_CR46 publication-title: Biometrics doi: 10.2307/2532705 – volume: 35 start-page: 772 issue: 2 year: 2007 ident: 9420_CR7 publication-title: Ann. Stat. doi: 10.1214/009053606000001307 – volume: 66 start-page: 319 year: 1971 ident: 9420_CR36 publication-title: J. Am. Stat. Assoc. doi: 10.1080/01621459.1971.10482261 – volume: 141 start-page: 1684 issue: 5 year: 2011 ident: 9420_CR44 publication-title: J. Stat. Plan. Inference doi: 10.1016/j.jspi.2010.11.031 – volume-title: Optimal Design year: 1980 ident: 9420_CR45 doi: 10.1007/978-94-009-5912-5 – volume-title: Algorithms for Worst-Case Design and Applications to Risk Management year: 2002 ident: 9420_CR43 – volume: 11 start-page: 403 year: 1980 ident: 9420_CR21 publication-title: Math. Oper.forsch. Stat., Ser. Stat. – volume: 31 start-page: 153 year: 1985 ident: 9420_CR18 publication-title: Math. Program. doi: 10.1007/BF02591747 – volume: 12 start-page: 115 year: 2002 ident: 9420_CR34 publication-title: Stat. Comput. doi: 10.1023/A:1014878317736 – volume: 44 start-page: 117 year: 1995 ident: 9420_CR35 publication-title: J. Stat. Plan. Inference doi: 10.1016/0378-3758(94)00042-T – volume: 65 start-page: 377 issue: 3 year: 2000 ident: 9420_CR3 publication-title: Psychometrika doi: 10.1007/BF02296152 – ident: 9420_CR31 – volume: 16 start-page: 203 year: 1974 ident: 9420_CR33 publication-title: Technometrics |
| SSID | ssj0011634 |
| Score | 2.1583428 |
| Snippet | Minimax optimal experimental designs are notoriously difficult to study largely because the optimality criterion is not differentiable and there is no... |
| SourceID | crossref springer |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 1063 |
| SubjectTerms | Artificial Intelligence Mathematics and Statistics Probability and Statistics in Computer Science Statistical Theory and Methods Statistics Statistics and Computing/Statistics Programs |
| Title | A semi-infinite programming based algorithm for finding minimax optimal designs for nonlinear models |
| URI | https://link.springer.com/article/10.1007/s11222-013-9420-6 |
| Volume | 24 |
| WOSCitedRecordID | wos000341440800011&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1573-1375 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0011634 issn: 0960-3174 databaseCode: RSV dateStart: 19970101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3PS8MwFH7o9DAPTqfi_EUOnpRCa5KmOQ5xeHEI_mC3kjapDtZN2in--b6k7cZABb30stc1JO_lfY-XfB_AOccUjUEmPSy9jMeo0Rhz-BAKSzFtAyrxndiEGA6j0Uje1_e4y-a0e9OSdDv18rJbgLnMs2oEktmaZx02uCWbsSX6w_OidYAAw3FGITTHDUawppX53V-sJqPVTqhLMIPOv4a2A9s1niT9ygF2Yc1Mu9BptBpIHbpd2Lpb8LOWXWhbjFlRNO-B7pPS5GMPfW1sESipz2zlOARis5wmavIyK8bz15wgxiWuz42_WVqSXH2SGW47OQ5Cu9MgpbOZVhQcqiBOa6fch6fBzeP1rVeLL3gp5dHc45kQVF9llIdYbxumKQ0R6vFQ-0pRrmQopUhClYhIS52YiCVXVAVcJNQK3yh6AC38lDkEkqXWEVjAlDZMGD_xM6ks0lMqyIIg7YHfrEKc1szkViBjEi85le0ExzjBsZ3gOOzBxeKVt4qW4zfjy2bZ4jpCy5-tj_5kfQxthFCsup14Aq158W5OYTP9wEUszpxnfgFvvd2s |
| linkProvider | Springer Nature |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3fS8MwED50Cs4Hp1Nx_syDT0qhXdJmfRzimLgNwSl7K2mT6mDdpJ3in-8lbTcGKuhLX3ZdQ3KX-45Lvg_g0sUUjUHmW1h6KYtRJTHm8MEFlmJSB1RoG7EJPhi0RiP_objHnZWn3cuWpNmpl5fdHMxlllYj8JmuedZhg2mVHV2iPz4vWgcIMAxnFEJz3GA4K1uZ3_3FajJa7YSaBNOp_Wtou7BT4EnSzh1gD9bUtA61UquBFKFbh-3-gp81q0NVY8yconkfZJtkKhlb6GtjjUBJcWYrwSEQneUkEZOXWTqevyYEMS4xfW78TdOSJOKTzHDbSXAQ0pwGyYzNNKfgECkxWjvZATx1boc3XasQX7Ai6rbmlhtzTmUzpq6H9bZiklIPoZ7rSVsI6grf830eeiLkLenLULVY2KTCcXlItfCNoIdQwU-pIyBxpB2BOUxIxbiyQzv2hUZ6Qjix40QNsMtVCKKCmVwLZEyCJaeynuAAJzjQExx4DbhavPKW03L8ZnxdLltQRGj2s_Xxn6wvYKs77PeC3t3g_gSqCKdYflPxFCrz9F2dwWb0gQuanhsv_QLcxOCQ |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8NAEB60itSD1apYn3vwpIQm3U22ORa1KGopvugtbLIbLTRtSaL4853No6WggnjJJZtk2Z3JfMPMfh_AqY0hGp3MNTD1UgajSqLP4YULTMWkdijfzMQmeK_XHgzcfqFzmpTd7mVJMj_ToFmaxmlzKsPm_OCbhXHN0MoELtP5zzKsMExkdE_Xw-PLrIyAYCPjj0KYjj8bzsqy5nevWAxMi1XRLNh0a_-e5iZsFDiTdHLD2IIlNa5DrdRwIIVL12H9fsbbmtShqrFnTt28DbJDEhUNDbTBoUampOjlinA6REc_ScTodRIP07eIIPYlWf0b72m6kkh8kgn-jiKchMy6RJJszDin5hAxyTR4kh147l49XVwbhSiDEVC7nRp2yDmVrZDaDubhiklKHYSAtiNNIagtXMd1ue8In7elK33VZn6LCsvmPtWCOILuQgU_pfaAhIE2EGYxIRXjyvTN0BUaAQphhZYVNMAsd8QLCsZyLZwx8uZcy3qBPVxgTy-w5zTgbPbINKfr-G3webmFXuG5yc-j9_80-gTW-pdd7-6md3sAVURZLD_AeAiVNH5XR7AafOB-xseZwX4BQSHpdA |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+semi-infinite+programming+based+algorithm+for+finding+minimax+optimal+designs+for+nonlinear+models&rft.jtitle=Statistics+and+computing&rft.au=Duarte%2C+Belmiro+P.+M.&rft.au=Wong%2C+Weng+Kee&rft.date=2014-11-01&rft.issn=0960-3174&rft.eissn=1573-1375&rft.volume=24&rft.issue=6&rft.spage=1063&rft.epage=1080&rft_id=info:doi/10.1007%2Fs11222-013-9420-6&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s11222_013_9420_6 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0960-3174&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0960-3174&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0960-3174&client=summon |