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Asymptotic normality of the optimal solution in multiresponse surface mathematical programming

dc.creatorDíaz-García J.A., Caro-Lopera F.J.spa
dc.date.accessioned2018-04-13T16:34:18Z
dc.date.available2018-04-13T16:34:18Z
dc.date.created2015
dc.identifier.issn18540023
dc.identifier.urihttp://hdl.handle.net/11407/4562
dc.description.abstractAn 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.eng
dc.language.isoeng
dc.publisherUniverza v Ljubljanispa
dc.relation.isversionofhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85011818223&partnerID=40&md5=3039f7c4129a4f8c948856d1ca714fdespa
dc.sourceScopusspa
dc.titleAsymptotic normality of the optimal solution in multiresponse surface mathematical programmingspa
dc.typeArticleeng
dc.rights.accessrightsinfo:eu-repo/semantics/restrictedAccess
dc.contributor.affiliationUniversidad Autónoma Agraria Antonio Narro, Calzada Antonio Narro 1923, Col. Buenavista, Saltillo, Coahuila, Mexico; Department of Basic Sciences, Universidad de Medellín, Medellín, Colombiaspa
dc.publisher.facultyFacultad de Ciencias Básicasspa
dc.abstractAn 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.eng
dc.creator.affiliationDíaz-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, Colombiaspa
dc.relation.ispartofesMetodoloski Zvezkispa
dc.relation.referencesAitchison, 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 Yorkspa
dc.type.versioninfo:eu-repo/semantics/publishedVersion
dc.type.driverinfo:eu-repo/semantics/article


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