59
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

On Non Overlapping Segmentation of the Response Surfaces for Solving Constrained Programming Problems Through Super Convergent Line Series

&
Pages 306-320 | Received 21 Dec 2011, Accepted 18 Jan 2012, Published online: 29 Aug 2013

References

  • Andrei , N. ( 2007 ). A scaled BEFS preconditioned conjugate algorithm for unconstrained optimization . Appl. Math. Lett. 20 : 645 – 650 .
  • Box , G. E. P. , Wilson , K. B. ( 1951 ). On the attainment of optimum conditions . J. Roy. Statist. Soc. Ser. B 13 : 1 – 45 .
  • Box , G. E. P. , Draper , N. R. ( 1959 ). A basis for the selection of a response surface design . J. Amer. Statist. Assoc. 54 : 622 – 654 .
  • Box , G. E. P. , Draper , N. R. ( 1987 ). Empirical Model-Building and Response Surface . New York : Wiley .
  • Childs , B. , Maron , M. J. ( 1976 ). An efficient Newton's method for optimization under equality constraints . Appl. Math. Computa. 2 : 273 – 282 .
  • Fletcher , R. , Powell , M. J. D. ( 1963 ). A rapidly convergent descent method for minimization . Comput. J. 7 : 149 – 154 .
  • Fletcher , R. , Reeves , C. M. ( 1964 ). Function minimization conjugate gradient . Comput. J. 7 : 149 – 154
  • Glover , F. ( 2010 ). The 3-2-3, stratified split and nested interval line search algorithms. Research Report, Optek Systems, Boulder, CO .
  • Grosan , C. , Abraham , A. ( 2007 ). Modified line search method for global optimization. In: Ams’07: Proc. of the First Asia Int. Conf. Model. Simul. IEEE Computer Society, Washington, D.C .
  • Hager , W. W. , Zhang , H. ( 2005 ). A new conjugate gradient method with guaranteed descent and an efficient line search . SIAM J. Optimiz. 16 : 170 – 192 .
  • Hager , W. E. , Zhang , H. ( 2006 ). A survey of non-linear conjugate gradient methods . Pacific J. Optimiz. 2 : 35 – 58 .
  • Hesse , R. ( 1973 ). A heuristic search procedure for estimating a global solution of non-convex programming problems . J. Operat. Res. 21 : 1267 – 1280 .
  • Hill , W. J. , Hunter , W. G. ( 1966 ). A review of response surface methodology, a literature survey . Technometrics 8 : 579 .
  • Hillier , F. S. , Lieberman , G. J. ( 1995 ). Introduction to Operation Research. , 6th ed. New York : McGraw Hill, Inc .
  • Idier , J. , Chouzenouk , E. , Moussaoui , S. (2009). A. majorize – minimize line search algorithm for barrier function optimization. 17th Society. European Signal Processing Conference, Washington, D.C.
  • Iwundu , M. P. , Offiong , A. ( 2003 ). An exchange algorithm for global optimization of a response function . Global J. Pure Appl. Sci. 9 : 147 – 153 .
  • Khuri , A. T. , Cornell , J. A. ( 1987 ). Response Surfaces . New York : Marcel Dekker .
  • Kwak , J. ( 2005 ). An application of Taguchi and response surface methodologies for geometric-error in surface grinding process . Int. Mach. 136 : 45 – 60 .
  • Labat , C. , Idier , J. ( 2008 ). Convergence of conjugate gradient methods with a closed-form stepwise formula . J. Optimiz. Theor. Applic. 136 : 45 – 60 .
  • Lind , E. E. , Goldin , J. , Hickman , J. B. ( 1960 ). Fitting field and cost response surface . Chem. Eng. Progr. 56 : 62 – 68 .
  • Mead , R. , Pike , D. J. ( 1975 ). A review of response surface methodology from a biometric view point . Biometrics 31 : 803 – 851 .
  • Montgomery , D. C. ( 1976 ). Design and Analysis of Experiments . Hoboken , NJ : John Wiley and Sons .
  • Montgomery , D. C. , Myers , R. H. , Vining , G. C. , Borror , C. M. , Kowalski , S. M. ( 2004 ). Response surface methodology: a retrospective and literature survey . J. Qual. Technol. 36 : 53 – 77 .
  • Myers , R. H. , Khuri , A. I. , Carter , W. H. ( 1989 ). Response Surface Methodology . New York : Wiley .
  • Onukogu , I. B. ( 1997 ). Foundation of Optimal Exploration of Response Surfaces . Nsukka : Ephrata Press .
  • Onukogu , I. B. , Chigbu , P. E. , (Eds). ( 2002 ). Super Convergent Line Series (in Optimal Design of Experiment and Mathematical Programming) . Nsukka : Ap Express Publishers .
  • Pazman , A. ( 1997 ). Foundations of Optimum Experimental Design . Boston : D-Reidal Publishing Company .
  • Raissi , S. ( 2009 ). Developing new processes and optimizing performance using response surface methodology . World Acad. Sci. Eng. Technol. 49 : 1039 – 1042 .
  • Rosenbrock , H. H. ( 1960 ). An automatic method for finding the greatest or least values of a function . Compu. J. 3 : 175 – 184 .
  • Storey , C. ( 1985 ). Mathematics in Industry. International Centre for Theoretical Physics, Trieste, Italy .
  • Sung , H. P. ( 1987 ). A class of multifactor of response surfaces . Technometrics 29 ( 4 ): 419 – 453 .
  • Taha , H. A. ( 1987 ). Operation Research: An Introduction. , 4th ed. New York : Macmillan Publishing Company .
  • Tui , H. ( 1964 ). Concave programming under linear constraint . Dokl. Akad. Naul SSR 159 : 32 – 35 .
  • Umoren , M. U. ( 1996 ). An experimental design method for solving linear programming problems. (Unpublished). Ph.D Thesis, Department of Statistics, University of Nigeria, Nsukka .
  • Umoren , M. U. ( 1999 ). A maximum norm exchange algorithm for solving solving linear programming problems . J. Nigeria Statist. Assoc. 13 : 39 – 56 .
  • Zwart , P. B. ( 1973 ). Non-linear programming counter examples to two Global Optimization Algorithms . J. Operat. Res. 21 : 1260 – 1266 .
  • Zwart , P. B. ( 1974 ). Global maximization of a convex function with linear inequality constraint . J. Operat. Res. 22 ( 3 ): 602 – 609 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.