Asymptotic normality of the optimal solution in multiresponse surface mathematical programming

An explicit form for the perturbation effect on the matrix of regression coefficients on the optimal solution in multiresponse surface methodology is obtained in this paper. Then, the sensitivity analysis of the optimal solution is studied and the critical point characterisation of the convex progra...

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2015
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Universidad de Medellín
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Repositorio UDEM
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eng
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oai:repository.udem.edu.co:11407/4562
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oai_identifier_str oai:repository.udem.edu.co:11407/4562
network_acronym_str REPOUDEM2
network_name_str Repositorio UDEM
repository_id_str
dc.title.spa.fl_str_mv Asymptotic normality of the optimal solution in multiresponse surface mathematical programming
title Asymptotic normality of the optimal solution in multiresponse surface mathematical programming
spellingShingle Asymptotic normality of the optimal solution in multiresponse surface mathematical programming
title_short Asymptotic normality of the optimal solution in multiresponse surface mathematical programming
title_full Asymptotic normality of the optimal solution in multiresponse surface mathematical programming
title_fullStr Asymptotic normality of the optimal solution in multiresponse surface mathematical programming
title_full_unstemmed Asymptotic normality of the optimal solution in multiresponse surface mathematical programming
title_sort Asymptotic normality of the optimal solution in multiresponse surface mathematical programming
dc.contributor.affiliation.spa.fl_str_mv Universidad Autónoma Agraria Antonio Narro, Calzada Antonio Narro 1923, Col. Buenavista, Saltillo, Coahuila, Mexico; Department of Basic Sciences, Universidad de Medellín, Medellín, Colombia
description An explicit form for the perturbation effect on the matrix of regression coefficients on the optimal solution in multiresponse surface methodology is obtained in this paper. Then, the sensitivity analysis of the optimal solution is studied and the critical point characterisation of the convex program, associated with the optimum of a multiresponse surface, is also analysed. Finally, the asymptotic normality of the optimal solution is derived by the standard methods.
publishDate 2015
dc.date.created.none.fl_str_mv 2015
dc.date.accessioned.none.fl_str_mv 2018-04-13T16:34:18Z
dc.date.available.none.fl_str_mv 2018-04-13T16:34:18Z
dc.type.eng.fl_str_mv Article
dc.type.coarversion.fl_str_mv http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_6501
http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.driver.none.fl_str_mv info:eu-repo/semantics/article
dc.identifier.issn.none.fl_str_mv 18540023
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/11407/4562
identifier_str_mv 18540023
url http://hdl.handle.net/11407/4562
dc.language.iso.none.fl_str_mv eng
language eng
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dc.relation.ispartofes.spa.fl_str_mv Metodoloski Zvezki
dc.relation.references.spa.fl_str_mv Aitchison, J., Silvey, S.D., Maximum likelihood estimation of parameters subject to restraints (1958) Annals of Mathematical Statistics, 29, pp. 813-828; Biles, W.E., A response surface method for experimental optimization of multi-response process (1975) Industrial & Engeneering Chemistry Process Design Development, 14, pp. 152-158; Gigelow, J.H., Shapiro, N.Z., Implicit function theorem for mathematical programming and for systems of iniqualities (1974) Mathematical Programming, 6 (2), pp. 141-156; Bishop, Y.M.M., Finberg, S.E., Holland, P.W., (1991) Discrete Multivariate Analysis: Theory and Practice, , The MIT press, Cambridge; Chatterjee, S., Hadi, A.S., (1988) Sensitivity Analysis in Linear Regression, , John Wiley: New York; Cramer, H., (1946) Mathematical Methods of Statistics, , Princeton University Press, Princeton; Díaz García, J.A., Ramos-Quiroga, R., An approach to optimization in response surfaces (2001) Communication in Statatistics, Part A-Theory and Methods, 30, pp. 827-835; Díaz García, J.A., Ramos-Quiroga, R., Erratum. An approach to optimization in response surfaces (2002) Communication in Statatistics, Part A-Theory and Methods, 31, p. 161; Dupačová, J., Stability in stochastic programming with recourse-estimated parameters (1984) Mathematical Programming, 28, pp. 72-83; Fiacco, A.V., Ghaemi, A., Sensitivity analysis of a nonlinear structural design problem (1982) Computers & Operations Research, 9 (1), pp. 29-55; Jagannathan, R., Minimax procedure for a class of linear programs under uncertainty (1977) Operations Research, 25, pp. 173-177; Kazemzadeh, R.B., Bashiri, M., Atkinson, A.C., Noorossana, R., A General Framework for Multiresponse Optimization Problems Based on Goal Programming (2008) European Journal of Operational Research, 189, pp. 421-429; Khuri, A.I., Conlon, M., Simultaneous optimization of multiple responses represented by polynomial regression functions (1981) Technometrics, 23, pp. 363-375; Khuri, A.I., Cornell, J.A., (1987) Response Surfaces: Designs and Analysis, , Marcel Dekker, Inc., NewYork; Miettinen, K.M., (1999) Non linear multiobjective optimization, , Kluwer Academic Publishers, Boston; Muirhead, R.J., (1982) Aspects of multivariate statistical theory, , Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, Inc., 1982; Myers, R.H., Montgomery, D.C., Anderson-Cook, C.M., (2009) Response surface methodology: Process and product optimization using designed experiments, , Third edition, Wiley, New York; Rao, C.R., (1973) Linear Statistical Inference and its Applications, , (2nd ed.) John Wiley & Sons, New York; Rao, S.S., (1979) Optimization Theory and Applications, , Wiley Eastern Limited, New Delhi; Ríos, S., Ríos Insua, S., Ríos Insua, M.J., (1989) Procesos de decisión Multicriterio, , EUDEMA, Madrid, (in Spanish); Steuer, R.E., (1986) Multiple criteria optimization: Theory, computation andappli-cations, , John Wiley, New York
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_16ec
rights_invalid_str_mv http://purl.org/coar/access_right/c_16ec
dc.publisher.spa.fl_str_mv Univerza v Ljubljani
dc.publisher.faculty.spa.fl_str_mv Facultad de Ciencias Básicas
dc.source.spa.fl_str_mv Scopus
institution Universidad de Medellín
repository.name.fl_str_mv Repositorio Institucional Universidad de Medellin
repository.mail.fl_str_mv repositorio@udem.edu.co
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spelling 2018-04-13T16:34:18Z2018-04-13T16:34:18Z201518540023http://hdl.handle.net/11407/4562An explicit form for the perturbation effect on the matrix of regression coefficients on the optimal solution in multiresponse surface methodology is obtained in this paper. Then, the sensitivity analysis of the optimal solution is studied and the critical point characterisation of the convex program, associated with the optimum of a multiresponse surface, is also analysed. Finally, the asymptotic normality of the optimal solution is derived by the standard methods.engUniverza v LjubljaniFacultad de Ciencias Básicashttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85011818223&partnerID=40&md5=3039f7c4129a4f8c948856d1ca714fdeMetodoloski ZvezkiAitchison, J., Silvey, S.D., Maximum likelihood estimation of parameters subject to restraints (1958) Annals of Mathematical Statistics, 29, pp. 813-828; Biles, W.E., A response surface method for experimental optimization of multi-response process (1975) Industrial & Engeneering Chemistry Process Design Development, 14, pp. 152-158; Gigelow, J.H., Shapiro, N.Z., Implicit function theorem for mathematical programming and for systems of iniqualities (1974) Mathematical Programming, 6 (2), pp. 141-156; Bishop, Y.M.M., Finberg, S.E., Holland, P.W., (1991) Discrete Multivariate Analysis: Theory and Practice, , The MIT press, Cambridge; Chatterjee, S., Hadi, A.S., (1988) Sensitivity Analysis in Linear Regression, , John Wiley: New York; Cramer, H., (1946) Mathematical Methods of Statistics, , Princeton University Press, Princeton; Díaz García, J.A., Ramos-Quiroga, R., An approach to optimization in response surfaces (2001) Communication in Statatistics, Part A-Theory and Methods, 30, pp. 827-835; Díaz García, J.A., Ramos-Quiroga, R., Erratum. An approach to optimization in response surfaces (2002) Communication in Statatistics, Part A-Theory and Methods, 31, p. 161; Dupačová, J., Stability in stochastic programming with recourse-estimated parameters (1984) Mathematical Programming, 28, pp. 72-83; Fiacco, A.V., Ghaemi, A., Sensitivity analysis of a nonlinear structural design problem (1982) Computers & Operations Research, 9 (1), pp. 29-55; Jagannathan, R., Minimax procedure for a class of linear programs under uncertainty (1977) Operations Research, 25, pp. 173-177; Kazemzadeh, R.B., Bashiri, M., Atkinson, A.C., Noorossana, R., A General Framework for Multiresponse Optimization Problems Based on Goal Programming (2008) European Journal of Operational Research, 189, pp. 421-429; Khuri, A.I., Conlon, M., Simultaneous optimization of multiple responses represented by polynomial regression functions (1981) Technometrics, 23, pp. 363-375; Khuri, A.I., Cornell, J.A., (1987) Response Surfaces: Designs and Analysis, , Marcel Dekker, Inc., NewYork; Miettinen, K.M., (1999) Non linear multiobjective optimization, , Kluwer Academic Publishers, Boston; Muirhead, R.J., (1982) Aspects of multivariate statistical theory, , Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, Inc., 1982; Myers, R.H., Montgomery, D.C., Anderson-Cook, C.M., (2009) Response surface methodology: Process and product optimization using designed experiments, , Third edition, Wiley, New York; Rao, C.R., (1973) Linear Statistical Inference and its Applications, , (2nd ed.) John Wiley & Sons, New York; Rao, S.S., (1979) Optimization Theory and Applications, , Wiley Eastern Limited, New Delhi; Ríos, S., Ríos Insua, S., Ríos Insua, M.J., (1989) Procesos de decisión Multicriterio, , EUDEMA, Madrid, (in Spanish); Steuer, R.E., (1986) Multiple criteria optimization: Theory, computation andappli-cations, , John Wiley, New YorkScopusAsymptotic normality of the optimal solution in multiresponse surface mathematical programmingArticleinfo:eu-repo/semantics/articlehttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Universidad Autónoma Agraria Antonio Narro, Calzada Antonio Narro 1923, Col. Buenavista, Saltillo, Coahuila, Mexico; Department of Basic Sciences, Universidad de Medellín, Medellín, ColombiaDíaz-García J.A., Caro-Lopera F.J.Díaz-García, J.A., Universidad Autónoma Agraria Antonio Narro, Calzada Antonio Narro 1923, Col. Buenavista, Saltillo, Coahuila, Mexico; Caro-Lopera, F.J., Department of Basic Sciences, Universidad de Medellín, Medellín, ColombiaAn explicit form for the perturbation effect on the matrix of regression coefficients on the optimal solution in multiresponse surface methodology is obtained in this paper. Then, the sensitivity analysis of the optimal solution is studied and the critical point characterisation of the convex program, associated with the optimum of a multiresponse surface, is also analysed. Finally, the asymptotic normality of the optimal solution is derived by the standard methods.http://purl.org/coar/access_right/c_16ec11407/4562oai:repository.udem.edu.co:11407/45622020-05-27 18:14:30.837Repositorio Institucional Universidad de Medellinrepositorio@udem.edu.co

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