Novel Interior Point Algorithms for Solving Nonlinear Convex Optimization Problems
This paper proposes three numerical algorithms based on Karmarkar’s interior point technique for solvingnonlinear convex programming problems subject to linear constraints. The first algorithm uses the Karmarkaridea and linearization of the objective function. The second and third algorithms are mod...
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| Veröffentlicht in: | Advances in Operations Research Jg. 2015; H. 2015; S. 59 - 65 |
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Cairo, Egypt
Hindawi Limiteds
01.01.2015
Hindawi Publishing Corporation John Wiley & Sons, Inc |
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| ISSN: | 1687-9147, 1687-9155 |
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| Abstract | This paper proposes three numerical algorithms based on Karmarkar’s interior point technique for solvingnonlinear convex programming problems subject to linear constraints. The first algorithm uses the Karmarkaridea and linearization of the objective function. The second and third algorithms are modification ofthe first algorithm using the Schrijver and Malek-Naseri approaches, respectively. These three novel schemesare tested against the algorithm of Kebiche-Keraghel-Yassine (KKY). It is shown that these three novel algorithmsare more efficient and converge to the correct optimal solution, while the KKY algorithm fails insome cases. Numerical results are given to illustrate the performance of the proposed algorithms. |
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| AbstractList | This paper proposes three numerical algorithms based on Karmarkar’s interior point technique for solving nonlinear convex programming problems subject to linear constraints. The first algorithm uses the Karmarkar idea and linearization of the objective function. The second and third algorithms are modification of the first algorithm using the Schrijver and Malek-Naseri approaches, respectively. These three novel schemes are tested against the algorithm of Kebiche-Keraghel-Yassine (KKY). It is shown that these three novel algorithms are more efficient and converge to the correct optimal solution, while the KKY algorithm fails in some cases. Numerical results are given to illustrate the performance of the proposed algorithms. This paper proposes three numerical algorithms based on Karmarkar’s interior point technique for solvingnonlinear convex programming problems subject to linear constraints. The first algorithm uses the Karmarkaridea and linearization of the objective function. The second and third algorithms are modification ofthe first algorithm using the Schrijver and Malek-Naseri approaches, respectively. These three novel schemesare tested against the algorithm of Kebiche-Keraghel-Yassine (KKY). It is shown that these three novel algorithmsare more efficient and converge to the correct optimal solution, while the KKY algorithm fails insome cases. Numerical results are given to illustrate the performance of the proposed algorithms. |
| Audience | Academic |
| Author | Hamidreza Navidi Alaeddin Malek Sakineh Tahmasebzadeh |
| Author_xml | – sequence: 1 fullname: Tahmasebzadeh, Sakineh – sequence: 2 fullname: Malek, Alaeddin – sequence: 3 fullname: Navidi, H. R. |
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| Cites_doi | 10.3923/jas.2009.3402.3406 10.1007/bf02579150 10.1016/j.disopt.2006.12.004 10.1016/j.amc.2007.03.066 10.1007/bf01587086 |
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| Copyright | Copyright © 2015 Sakineh Tahmasebzadeh et al. COPYRIGHT 2015 John Wiley & Sons, Inc. Copyright © 2015 Sakineh Tahmasebzadeh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
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| References | (1) 1984; 4 (2) 2009; 9 Schrijver A. Theory of Linear and Integer Programming 1986 New York, NY, USA John Wiley & Sons MR874114 Bazzara M. S. Jarvis J. Sherali H. D. Linear Programming and Network Flows 1984 New York, NY, USA John Wiley & Sons (12) 2007; 193 Hamdy A. T. Operations Research 1992 New York, NY, USA Macmillan MR856022 (5) 2008; 5 (8) 2004; 6 (11) 2009; 38 (9) 1989; 44 (10) 2012; 57 Roos C. Terlaky T. Vial J. Theory and Algorithms for Linear Optimization 2001 Princton University 12 5 (1) 1984 6 7 (4) 1992 (11) 1986 9 (10) 2001 (2) 2012; 57 (3) 2009; 38 |
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| SubjectTerms | Algorithms Analysis Convex programming Linear programming Mathematical optimization Methods Operations research Optimization Simplex method |
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| Title | Novel Interior Point Algorithms for Solving Nonlinear Convex Optimization Problems |
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