A bi-objective programming has been proposed for dealing with decision process involving two decision makers. In this paper, a bi-objective programming problem in which both objective functions are definite quadratic is considered. The feasible region is assumed to be a convex polyhedron. Solution methods namely; using KKT Conditions is developed. Illustrative examples for the method are presented and theorems and facts to support the method are also discussed. The solution of the examples are obtained using a LINGO (15.0) mathematical software.
| Published in | Mathematical Modelling and Applications (Volume 2, Issue 2) |
| DOI | 10.11648/j.mma.20170202.12 |
| Page(s) | 21-27 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Bi-Objective Programming, Definite Quadratic Programming, Quadratic Programming, KKT Conditions
| [1] | Benoit C. Chachuat. 2007. Nonlinear and dynamic optimization, IC-32: Winter Semister. |
| [2] | Etoa, J. B. E. 2011. Solving quadratic convex bi-level programming problems using a smooth method, Applied Mathematics and Computation, 217 (15): 6680-6690. |
| [3] | Hosseini, E. and Isa Nakhai, I, K. 2014. Taylor approach for solving nonlinear bi-level programming, 3 (11): 2322-5157. |
| [4] | Jin Hyuk Jung. 2008. Adaptive constraint reduction for convex quadratic programming and training support vector machines, University of Maryland. |
| [5] | Kalyanmoy Deb. Multi-objective optimization using evolutionary algorithm, Indian Institute of Technology, Kanpur, India, 48-53. |
| [6] | Liu, G. P., Yang, J. B. and Whidborne, J. F. 2003. Multi-objective Optimization and Control, Research Studies Press LTD. Baldock, Hertfordshire, England, 73-82. |
| [7] | Maria M. Seron. 2004. Optimality condition, Center for Complex Dynamics Systems and Control, University of Newcastle, Australia. |
| [8] | Narang, R. and Arora, S. R. 2009. Indefinite quadratic integer bi-level programming problem with bounded variable, Journal of Operational Research Society of India (OPEARCH), 46 (4): 428-448. |
| [9] | Ritu Arora and S. R. Arora. 2009. Indefinite quadratic programming problem with multi-objectives at both levels, International Journal of Optimization: Theory, Methods and Applications, 1 (3): 318-327. |
| [10] | Wang, Y. P. and Li, H. C. 2011. Agenetic algorithm for solving linear-quadratic programming problems, Advances Materials Research, 186: 626-630. |
APA Style
Amanu Gashaw, Getinet Alemayehu. (2017). Solving Definite Quadratic Bi-Objective Programming Problems by KKT Conditions. Mathematical Modelling and Applications, 2(2), 21-27. https://doi.org/10.11648/j.mma.20170202.12
ACS Style
Amanu Gashaw; Getinet Alemayehu. Solving Definite Quadratic Bi-Objective Programming Problems by KKT Conditions. Math. Model. Appl. 2017, 2(2), 21-27. doi: 10.11648/j.mma.20170202.12
AMA Style
Amanu Gashaw, Getinet Alemayehu. Solving Definite Quadratic Bi-Objective Programming Problems by KKT Conditions. Math Model Appl. 2017;2(2):21-27. doi: 10.11648/j.mma.20170202.12
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Download@article{10.11648/j.mma.20170202.12,
author = {Amanu Gashaw and Getinet Alemayehu},
title = {Solving Definite Quadratic Bi-Objective Programming Problems by KKT Conditions},
journal = {Mathematical Modelling and Applications},
volume = {2},
number = {2},
pages = {21-27},
doi = {10.11648/j.mma.20170202.12},
url = {https://doi.org/10.11648/j.mma.20170202.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20170202.12},
abstract = {A bi-objective programming has been proposed for dealing with decision process involving two decision makers. In this paper, a bi-objective programming problem in which both objective functions are definite quadratic is considered. The feasible region is assumed to be a convex polyhedron. Solution methods namely; using KKT Conditions is developed. Illustrative examples for the method are presented and theorems and facts to support the method are also discussed. The solution of the examples are obtained using a LINGO (15.0) mathematical software.},
year = {2017}
}
TY - JOUR T1 - Solving Definite Quadratic Bi-Objective Programming Problems by KKT Conditions AU - Amanu Gashaw AU - Getinet Alemayehu Y1 - 2017/04/25 PY - 2017 N1 - https://doi.org/10.11648/j.mma.20170202.12 DO - 10.11648/j.mma.20170202.12 T2 - Mathematical Modelling and Applications JF - Mathematical Modelling and Applications JO - Mathematical Modelling and Applications SP - 21 EP - 27 PB - Science Publishing Group SN - 2575-1794 UR - https://doi.org/10.11648/j.mma.20170202.12 AB - A bi-objective programming has been proposed for dealing with decision process involving two decision makers. In this paper, a bi-objective programming problem in which both objective functions are definite quadratic is considered. The feasible region is assumed to be a convex polyhedron. Solution methods namely; using KKT Conditions is developed. Illustrative examples for the method are presented and theorems and facts to support the method are also discussed. The solution of the examples are obtained using a LINGO (15.0) mathematical software. VL - 2 IS - 2 ER -
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