This work has successfully shown that the optimum of a quadratic response function with zero coefficients except that of the quadratic term lies at the origin. This was achieved by using optimal designs technique for solving unconstrained optimization problems with quadratic surfaces. In just one move, the objective of the work, that is, xmin = 0 was realized.
References
[1]
Eiselt, H.A., Pederzoli, G. and Sandblom, C.L. (1987) Continuous Optimization Models. Walter de Gruyter & Co., Berlin.
[2]
Taha, H.A. (2005) Operations Research: An Introduction. 7th Edition, Pearson Education, Singapore Pte. Ltd., Indian Branch, Delhi.
[3]
Etukudo, I. (2017) Optimal Designs Technique for Locating the Optimum of a Second Order Response Function. American Journal of Operations Research, 7, 263-271. https://doi.org/10.4236/ajor.2017.75018
[4]
Singh, S.K., Yadav, P. and Mukherjee. (2015) Line Search Techniques by Fibonacci Search. International Journal of Mathematics and Statistics Invention, 3, 27-29.
[5]
Winston, W.L. (1994) Operations Research: Applications and Algorithms. 3rd Edition, Duxbury Press, Wadsworth Publishing Company, Belmont, CA.
[6]
Gerald, C.F. and Wheatley, P. (2004) Applied Numerical Analysis. 7th Edition, Addison-Wesley, Boston.
[7]
Taha, H.A. (2007) Operations Research: An Introduction. 8th Edition, Asoke K. Ghosh, Prentice Hall of India, Delhi.
[8]
Subasi, M., Yildirim, N. and Yildirim, B. (2004) An Improvement on Fibonacci Search Method in Optimization Theory. Applied Mathematics and Computation, Elsevier, 147, 893-901.
[9]
Hassin, R. (1981) On Maximizing Functions by Fibonacci Search.
[10]
Etukudo, I.A. (2017) Optimal Designs Technique for Solving Unconstrained Optimization Problems with Univariate Quadratic Surfaces. American Journal of Computational and Applied Mathematics, 7, 33-36.
[11]
Onukogu, I.B. (2002) Super Convergent Line Series in Optimal Design on Experimental and Mathematical Programming. AP Express Publisher, Nigeria.
[12]
Onukogu, I.B. (1997) Foundations of Optimal Exploration of Response Surfaces. Ephrata Press, Nsukka.
[13]
Etukudo, I.A. and Umoren, M.U. (2008) A Modified Super Convergent Line Series Algorithm for Solving Linear Programming Problems. Journal of Mathematical Sciences, 19, 73-88.
[14]
Umoren, M.U. and Etukudo, I.A. (2010) A Modified Super Convergent Line Series Algorithm for Solving Unconstrained Optimization Problems. Journal of Modern Mathematics and Statistics, 4, 115-122.
https://doi.org/10.3923/jmmstat.2010.115.122
[15]
Umoren, M.U. and Etukudo, I.A. (2009) A Modified Super Convergent Line Series Algorithm for Solving Quadratic Programming Problems. Journal of Mathematical Sciences, 20, 55-66.
