Subscribe

Subscribe to our Newsletter and get informed about new publication regulary and special discounts for subscribers!

BSMaSS > BSMaSS Volume 5 > A Note on Convex Programming in Practical Problems
< Back to Volume

A Note on Convex Programming in Practical Problems

Full Text PDF

Abstract:

In recent years, convex programming has become a sophisticated tool ofcentral importance in engineering, finance, operations research, statistics etc. The goalof this paper is to emphasize modeling and present several convex programmingproblem formulations especially in optimal design and location theory. We buildsimple models to address this question, investigate their properties and apply a variantof the Weierstrass theorem to prove the existence of a solution. Our results extend andimprove some other comparable results of the author [2,8,20,21,22,23,24,25].

Info:

Periodical:
The Bulletin of Society for Mathematical Services and Standards (Volume 5)
Pages:
19-26
Citation:
I. A. Osinuga and D. A. Agunbiade, "A Note on Convex Programming in Practical Problems", The Bulletin of Society for Mathematical Services and Standards, Vol. 5, pp. 19-26, 2013
Online since:
March 2013
Export:
Distribution:
References:

Atashgar, A.B., Seifi, A.: Optimal design of multi-response experiments using semi-definite programming, Optim. Eng., 10, 75-90 (2009).

Atieg, A., Watson, G.A.: Use of Anziam J., 45 4, C187-C200 (2004). l p norms in fitting curves and surfaces to data.

Bector, C.R., Chandra, S., Dutta, J.: Principles of optimization theory, Narosa publishing house, New Delhi, (2005).

Boyd, S., Vanderberghe, L.: CRCD programme: Convex optimization for engineering analysis and design, Proceedings of the American control conference, Seetle, Washington, (1996).

Boyd, S., Vanderberghe, L.: Convex optimization, Cambridge University press, Cambridge, (http: /www. stanford. edu/~boyd/cvxbook), (2004).

Butt, S.E., Cavalier, T.M.: An efficient algorithms for facility location in the presence of forbidden regions, Eur.J. Oper. Res., 90, 56-70 (1996).

Chares, R., Glineur, F.: An interior-point method for the single facility location problem with mixed norms using a conic formulation, Ecore discussion paper, Universite Catholique de Louvain, (2007).

Chowell, G., Nishiura, H and Bettencourt, L.M.A.: Comparative estimation of the reproduction number for pandemic influenza from daily case notification data, J.R. Soc. Interface, 4, 155-166 (2007).

Dasarathy, R., White, L.J.: A maxmin location problem, Oper. Res., 28 6, 1385-1401 (1980).

Drezner, Z., Klamroth, K., Schobel, A and Wesolowsky, G.O.: The Weber Problem, In: Z. Drezner, H.W. Hamacher (Eds. ): Location analysis: Applications and theory, 1-36, Springer Verlag, (2002).

Drezner, Z., Scott, C. and Song, J-S.: The central warehouse location problem revisited, IMA J. Mgt. Math., 14, 321-326 (2003).

Ferreira, P.S.G.: The existence and uniqueness of the minimum norm solution to certain linear and nonlinear problems, Signal Processing, 55, 137-139 (1996).

Hindi, H.: A tutorial on convex optimization, Palo Alto research centre (PARC), Palo Alto, California [online] available at http: /www2. parc. com/spl/members/hhindi/reports/CvxOptTutPaper. pdf, accessed 5 October, (2010).

Kanzow, C., Qi, H. and Qi, L.: On the minimum norm solution of linear programs, Applied Math. Report, AMR00 14, 1-11 (2000).

Kocak, H.: Convex programming approach to the shopping mall (AVM) site selection problem and Sakarya, Eur.J. Social Sc. 13 2, 219-228 (2010).

Kreyszig, E.: Introductory functional analysis with applications(student edition), John Wiley, Singapore, (2005).

Kuhn, H.W.: A note on Fermat's problem, Mathematical Programming, 4, 98-107 (1973).

Love, F.R., Morris, J. G and Wesolowsky, G.O.: Facilities location: models and methods, Elsevier, New York, (1988).

Moarref, M., Sayyaadi, H.: Facility location optimization via multi-agent robotic systems, IEEE Trans. Robotics Automation, (2008).

Oniyide, O.R., Osinuga, I.A.: On the existence of best sample in simple random sampling, J. Math. Assoc. Nigeria, 33 2b, 290-294 (2006).

Osinuga, I.A., Oniyide, O.R.: An overview of norm approximation applications, Far East J. Math. Sci., 43 2, 189-202 (2010).

Sciences Association) Conference, Windhoek, Namibia, 2, 54-60 (2007).

Schandl, B., Klamroth, K. and Wiecek, M.M.: Norm-based approximation in bicriteria programming, Computational Optim. Appl., 20, 23-42 (2001).

Schandl, B., Klamroth, K. and Wiecek, M.M.: Norm-based approximation in convex multicriteria programming, In: B. Freischmann, R. Lasch, U. Derigs, W. Domshke and U. Rieder (Eds. ): Operations Research Proceedings 2000, 8-13, Springer Verlag, (2001).

Schandl, B., Klamroth, K. and Wiecek, M.M.: Norm-based approximation in multicriteria programming, Computers Math. Appl., 44, 925-942 (2002).

Srebro, R.: Iterative refinement of the minimum norm solution of the bioelectric inverse problem, IEEE Trans. Biomedical Eng., 43 5, 547-552 (1996).

Sundaram, R.K.: A first course in optimization theory, Cambridge University press, New York, (1996).

Wesolowsky, G.O.: The Weber problem: History and Perspectives, Location Science, 1, 5-23 (1992).

Show More Hide
Cited By:
This article has no citations.