Approximate solution algorithm for multi-parametric non-convex programming problems with polyhedral constraints

Authors

  • Abay Molla Kassa Addis Ababa Institute of Technology, Addis Ababa University, P.O.Box 1176, Addis Ababa
  • Semu Mitiku Kassa Addis Ababa University P.O.Box 1176, Addis Ababa

DOI:

https://doi.org/10.11121/ijocta.01.2014.00171

Keywords:

Multi-parametric Programming, Convex relaxation

Abstract

In this paper, we developed a novel algorithmic approach for thesolution of multi-parametric non-convex programming problems withcontinuous decision variables. The basic idea of the proposedapproach is based on successive convex relaxation of each non-convexterms and sensitivity analysis theory. The proposed algorithm isimplemented using MATLAB software package and numericalexamples are presented to illustrate the effectiveness andapplicability of the proposed method on multi-parametric non-convexprogramming problems with polyhedral constraints.

Author Biographies

Abay Molla Kassa, Addis Ababa Institute of Technology, Addis Ababa University, P.O.Box 1176, Addis Ababa

Department of Chemical Engineering,

Addis Ababa Institute of Technology

P.O.Box 1176, Addis Ababa

Semu Mitiku Kassa, Addis Ababa University P.O.Box 1176, Addis Ababa

Associate Professor of Applied Mathemiacs,

Addis Ababa University

References

Li Z. and Ierapetritou G. M., A New Methodology for the General Multiparametric Mixed-Integer Linear Programming (MILP) Problems, Industrial & Engineering Chemistry Research, 46, 5141-5151 (2007). CrossRef

Dua V. Bozinis A. N. and Pistikopoulos N. E., A multi-parametric Programming Approach for mixed-integer quadratic engineering problems, Computers & Chemical Engineering, 26, 715-733 (2002). CrossRef

Pistikopous, N. E., Georgiads C. M. and Dua V., (Ed-itors) Multiparametric programming: Theory, algorithm, and application, WILEY-VCH Verlag GmbH and Co. KGaA, (2007).

Dua V., Pistikopoulos, E. N., An algorithm for the solution of multiparametric mixed integer linear programming problems, Annals of Operations Research, 99, 123 - 139 (2001). CrossRef

Fa’ısca P. N, Dua V., Rustem B., Saraiva M. P., Pistikopoulos N. E., Parametric global optimisation for bilevel programming, Journal of Global Optimization, 38, 609-623 (2006). CrossRef

Fa’ısca P. N., Saraiva M. P., Rustem B., Pistikopoulos N. E. A multiparametric programming approach for multilevel hierarchical and decentralized optimization problems, Computational Management Science, 6, 377-397 (2009). CrossRef

Tøndel P., Johansen T. A. and Bemporad A., Further Results on Multiparametric Quadratic Programming, in Proceedings of 42nd IEEE Conference on Decision and Control, 3, 3173-3178 (2003).

Al-Khayyal A. F., Jointly constrained bilinear programms and related problems: An overview, Computers Math. Applic, 19, 53-62 (1990).

Adjiman S. C., Dallwing S., Floudas A. C., Neumaier A., A global optimization method, αBB, for general twice-differentiable constrained NLPs I.Theoretical advances, Computers and Chemical Engineering, 22, 1137 - 1158 (1998). CrossRef

Androulakis P. I., Maranas D. C., and Floudas A. C., αBB: A Global Optimization Method for General Constrained Nonconvex Problems, Journal of Global Optimization, 7, 337-363 (1995). CrossRef

Fiacco V. A., Sensitivity analysis for nonlinear programming using penalty methods, Mathematical Programming, 10, 287-311 (1976). CrossRef

Fiacco V. A., Introduction to Sensitivity and Stability Analysis in Nonlinear Programming, Academic press, (1983).

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Published

2014-06-12

How to Cite

Kassa, A. M., & Kassa, S. M. (2014). Approximate solution algorithm for multi-parametric non-convex programming problems with polyhedral constraints. An International Journal of Optimization and Control: Theories &Amp; Applications (IJOCTA), 4(2), 89–98. https://doi.org/10.11121/ijocta.01.2014.00171

Issue

Section

Optimization & Applications