Asymptotic Normality of the Optimal Solution in Multiresponse Surface Mathematical Programming

An explicit form for the perturbation effect on the matrix of regression coeffi- cients 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 prog...

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Fecha de publicación:
2015
Institución:
Universidad de Medellín
Repositorio:
Repositorio UDEM
Idioma:
eng
OAI Identifier:
oai:repository.udem.edu.co:11407/3471
Acceso en línea:
http://hdl.handle.net/11407/3471
Palabra clave:
Asymptotic normality
Multiresponse surface optimisation
Sensitivity analysis
Mathematical programming
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openAccess
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http://purl.org/coar/access_right/c_abf2
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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
Asymptotic normality
Multiresponse surface optimisation
Sensitivity analysis
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.subject.spa.fl_str_mv Asymptotic normality
Multiresponse surface optimisation
Sensitivity analysis
Mathematical programming
topic Asymptotic normality
Multiresponse surface optimisation
Sensitivity analysis
Mathematical programming
description An explicit form for the perturbation effect on the matrix of regression coeffi- cients 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 2017-06-15T22:05:23Z
dc.date.available.none.fl_str_mv 2017-06-15T22:05:23Z
dc.type.eng.fl_str_mv Article
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.citation.spa.fl_str_mv Díaz-García, J. A., & Caro-Lopera, F. J. (2015). Asymptotic Normality of the Optimal Solution in Multiresponse Surface Mathematical Programming. Metodoloski Zvezki, 12(1), 11-24
dc.identifier.issn.none.fl_str_mv 18540023
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/11407/3471
dc.identifier.eissn.none.fl_str_mv 18540031
identifier_str_mv Díaz-García, J. A., & Caro-Lopera, F. J. (2015). Asymptotic Normality of the Optimal Solution in Multiresponse Surface Mathematical Programming. Metodoloski Zvezki, 12(1), 11-24
18540023
18540031
url http://hdl.handle.net/11407/3471
dc.language.iso.none.fl_str_mv eng
language eng
dc.relation.isversionof.spa.fl_str_mv http://www.stat-d.si/mz/mz12.12/Diaz2015.pdf
dc.relation.ispartofes.spa.fl_str_mv Metodoloski zvezki, Vol. 12, No. 1, 2015, 11-24
dc.relation.references.spa.fl_str_mv Aitchison, J. and S. D. Silvey, S. D. (1958): Maximum likelihood estimation of parameters subject to restraints. Annals of Mathematical Statistics, 29, 813–828.
Biles, W. E. (1975): A response surface method for experimental optimization of multi-response process. Industrial & Engeneering Chemistry Process Design Development, 14, 152-158.
Gigelow, J. H. and Shapiro, N. Z. (1974): Implicit function theorem for mathematical programming and for systems of iniqualities. Mathematical Programming, 6(2), 141– 156.
Bishop, Y. M. M., Finberg, S. E. and Holland, P. W. (1991): Discrete Multivariate Analysis: Theory and Practice. The MIT press, Cambridge.
Chatterjee, S. and Hadi, A. S. (1988): Sensitivity Analysis in Linear Regression. John Wiley: New York.
Cramer, H. (1946): ´ Mathematical Methods of Statistics. Princeton University Press, Princeton.
D´ıaz Garc´ıa, J. A. and Ramos-Quiroga, R. (2001): An approach to optimization in response surfaces. Communication in Statatistics, Part A- Theory and Methods, 30, 827–835.
D´ıaz Garc´ıa, J. A. and Ramos-Quiroga, R. (2002): Erratum. An approach to optimization in response surfaces. Communication in Statatistics, Part A- Theory and Methods, 31, 161.
Dupacov ˇ a, J. (1984): Stability in stochastic programming with recourse-estimated ´ parameters. Mathematical Programming, 28, 72–83.
Fiacco, A. V. and Ghaemi, A. (1982): Sensitivity analysis of a nonlinear structural design problem. Computers & Operations Research, 9(1), 29–55.
Jagannathan, R. (1977): Minimax procedure for a class of linear programs under uncertainty. Operations Research, 25, 173–177.
Kazemzadeh, R. B., Bashiri, M., Atkinson, A. C. and Noorossana, R. (2008): A General Framework for Multiresponse Optimization Problems Based on Goal Programming. European Journal of Operational Research, 189, 421-429.
Khuri, A. I. and Conlon, M. (1981): Simultaneous optimization of multiple responses represented by polynomial regression functions. Technometrics, 23, 363–375.
Khuri, A. I. and 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. and 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.
R´ıos, S., R´ıos Insua, S. and R´ıos Insua, M. J. (1989): Procesos de decision Multicri- ´ terio. EUDEMA, Madrid, (in Spanish).
Steuer, R. E. (1986): Multiple criteria optimization: Theory, computation and applications. John Wiley, New York.
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dc.publisher.spa.fl_str_mv Faculty of Social Sciences, University of Ljubljana
dc.publisher.program.spa.fl_str_mv Tronco común Ingenierías
dc.publisher.faculty.spa.fl_str_mv Facultad de Ciencias Básicas
dc.source.spa.fl_str_mv Metodoloski Zvezki
institution Universidad de Medellín
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spelling 2017-06-15T22:05:23Z2017-06-15T22:05:23Z2015Díaz-García, J. A., & Caro-Lopera, F. J. (2015). Asymptotic Normality of the Optimal Solution in Multiresponse Surface Mathematical Programming. Metodoloski Zvezki, 12(1), 11-2418540023http://hdl.handle.net/11407/347118540031An explicit form for the perturbation effect on the matrix of regression coeffi- cients 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.engFaculty of Social Sciences, University of LjubljanaTronco común IngenieríasFacultad de Ciencias Básicashttp://www.stat-d.si/mz/mz12.12/Diaz2015.pdfMetodoloski zvezki, Vol. 12, No. 1, 2015, 11-24Aitchison, J. and S. D. Silvey, S. D. (1958): Maximum likelihood estimation of parameters subject to restraints. Annals of Mathematical Statistics, 29, 813–828.Biles, W. E. (1975): A response surface method for experimental optimization of multi-response process. Industrial & Engeneering Chemistry Process Design Development, 14, 152-158.Gigelow, J. H. and Shapiro, N. Z. (1974): Implicit function theorem for mathematical programming and for systems of iniqualities. Mathematical Programming, 6(2), 141– 156.Bishop, Y. M. M., Finberg, S. E. and Holland, P. W. (1991): Discrete Multivariate Analysis: Theory and Practice. The MIT press, Cambridge.Chatterjee, S. and Hadi, A. S. (1988): Sensitivity Analysis in Linear Regression. John Wiley: New York.Cramer, H. (1946): ´ Mathematical Methods of Statistics. Princeton University Press, Princeton.D´ıaz Garc´ıa, J. A. and Ramos-Quiroga, R. (2001): An approach to optimization in response surfaces. Communication in Statatistics, Part A- Theory and Methods, 30, 827–835.D´ıaz Garc´ıa, J. A. and Ramos-Quiroga, R. (2002): Erratum. An approach to optimization in response surfaces. Communication in Statatistics, Part A- Theory and Methods, 31, 161.Dupacov ˇ a, J. (1984): Stability in stochastic programming with recourse-estimated ´ parameters. Mathematical Programming, 28, 72–83.Fiacco, A. V. and Ghaemi, A. (1982): Sensitivity analysis of a nonlinear structural design problem. Computers & Operations Research, 9(1), 29–55.Jagannathan, R. (1977): Minimax procedure for a class of linear programs under uncertainty. Operations Research, 25, 173–177.Kazemzadeh, R. B., Bashiri, M., Atkinson, A. C. and Noorossana, R. (2008): A General Framework for Multiresponse Optimization Problems Based on Goal Programming. European Journal of Operational Research, 189, 421-429.Khuri, A. I. and Conlon, M. (1981): Simultaneous optimization of multiple responses represented by polynomial regression functions. Technometrics, 23, 363–375.Khuri, A. I. and 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. and 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.R´ıos, S., R´ıos Insua, S. and R´ıos Insua, M. J. (1989): Procesos de decision Multicri- ´ terio. EUDEMA, Madrid, (in Spanish).Steuer, R. E. (1986): Multiple criteria optimization: Theory, computation and applications. John Wiley, New York.Metodoloski ZvezkiAsymptotic normalityMultiresponse surface optimisationSensitivity analysisMathematical programmingAsymptotic Normality of the Optimal Solution in Multiresponse Surface Mathematical ProgrammingArticleinfo:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Díaz-García, José A.Caro-Lopera, Francisco J.Díaz-García, José A.; Universidad Autónoma Agraria Antonio NarroCaro-Lopera, Francisco J.; Universidad de MedellínORIGINALArticulo_.htmlArticulo_.htmlVer PDF en página del publicadortext/html545http://repository.udem.edu.co/bitstream/11407/3471/1/Articulo_.htmlfd2929e11464534ee322cf72a8a9fab1MD51THUMBNAILportada.pngportada.pngimage/png19702http://repository.udem.edu.co/bitstream/11407/3471/2/portada.png0fa31f46a9ad98bf42d9487c92a04205MD5211407/3471oai:repository.udem.edu.co:11407/34712020-05-27 18:32:39.273Repositorio Institucional Universidad de Medellinrepositorio@udem.edu.co

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