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Solving Definite Quadratic Bi-Objective Programming Problems by KKT Conditions

Received: 27 June 2016     Accepted: 11 July 2016     Published: 25 April 2017
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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.

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.

Copyright

Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Bi-Objective Programming, Definite Quadratic Programming, Quadratic Programming, KKT Conditions

References
[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.
Cite This Article
  • 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

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    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

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    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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  • @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}
    }
    

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    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
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    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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Author Information
  • Department of Mathematics, College of Natural Science, Arba Minch University, Arba Minch, Ethiopia

  • Department of Mathematics, College of Natural Science, Haramaya University, Haramaya, Ethiopia

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