This paper introduces a weighted analytic center for a system of second order cone constraints. The associated barrier function is shown to be convex and conjugate gradient (CG) methods are used to compute the weighted analytic center. In contrast with Newton’s-like methods, CG methods use only the gradient and not the Hessian to minimize a function. The methods considered are the HPRP and ZA with exact and inexact line searches. The exact line search uses Newton’s method and quadratic interpolation is used for the inexact line search. The performance of each method on random test problems was evaluated by observing the number of iterations and time required to find the weighted analytic center. Our numerical methods indicate that ZA is better than HPRP with any of the two line searches, in terms of the number of iterations and time to find the weighted analytic center. Quadratic interpolation inexact line search gives the best success rate and fewest number of iterations for the CG methods considered. On the other hand, the fastest time for the CG methods is found with the Newton’s exact line search. In addition, these results indicate that for each of the methods, our Quadratic interpolation inexact line search has a higher cost per iteration than that of the Newton’s exact line search.
| Published in | Applied and Computational Mathematics (Volume 10, Issue 6) |
| DOI | 10.11648/j.acm.20211006.13 |
| Page(s) | 146-155 |
| 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 |
Second-Order Cone Constraints, Weighted Analytic Center, Conjugate Gradient Methods, Interior-point Methods
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APA Style
Bamanga Dawuda, Shafiu Jibrin, Ibrahim Abdullahi. (2021). A Weighted Analytic Center for Second-Order Cone Constraints. Applied and Computational Mathematics, 10(6), 146-155. https://doi.org/10.11648/j.acm.20211006.13
ACS Style
Bamanga Dawuda; Shafiu Jibrin; Ibrahim Abdullahi. A Weighted Analytic Center for Second-Order Cone Constraints. Appl. Comput. Math. 2021, 10(6), 146-155. doi: 10.11648/j.acm.20211006.13
AMA Style
Bamanga Dawuda, Shafiu Jibrin, Ibrahim Abdullahi. A Weighted Analytic Center for Second-Order Cone Constraints. Appl Comput Math. 2021;10(6):146-155. doi: 10.11648/j.acm.20211006.13
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Download@article{10.11648/j.acm.20211006.13,
author = {Bamanga Dawuda and Shafiu Jibrin and Ibrahim Abdullahi},
title = {A Weighted Analytic Center for Second-Order Cone Constraints},
journal = {Applied and Computational Mathematics},
volume = {10},
number = {6},
pages = {146-155},
doi = {10.11648/j.acm.20211006.13},
url = {https://doi.org/10.11648/j.acm.20211006.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20211006.13},
abstract = {This paper introduces a weighted analytic center for a system of second order cone constraints. The associated barrier function is shown to be convex and conjugate gradient (CG) methods are used to compute the weighted analytic center. In contrast with Newton’s-like methods, CG methods use only the gradient and not the Hessian to minimize a function. The methods considered are the HPRP and ZA with exact and inexact line searches. The exact line search uses Newton’s method and quadratic interpolation is used for the inexact line search. The performance of each method on random test problems was evaluated by observing the number of iterations and time required to find the weighted analytic center. Our numerical methods indicate that ZA is better than HPRP with any of the two line searches, in terms of the number of iterations and time to find the weighted analytic center. Quadratic interpolation inexact line search gives the best success rate and fewest number of iterations for the CG methods considered. On the other hand, the fastest time for the CG methods is found with the Newton’s exact line search. In addition, these results indicate that for each of the methods, our Quadratic interpolation inexact line search has a higher cost per iteration than that of the Newton’s exact line search.},
year = {2021}
}
TY - JOUR T1 - A Weighted Analytic Center for Second-Order Cone Constraints AU - Bamanga Dawuda AU - Shafiu Jibrin AU - Ibrahim Abdullahi Y1 - 2021/11/27 PY - 2021 N1 - https://doi.org/10.11648/j.acm.20211006.13 DO - 10.11648/j.acm.20211006.13 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 146 EP - 155 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20211006.13 AB - This paper introduces a weighted analytic center for a system of second order cone constraints. The associated barrier function is shown to be convex and conjugate gradient (CG) methods are used to compute the weighted analytic center. In contrast with Newton’s-like methods, CG methods use only the gradient and not the Hessian to minimize a function. The methods considered are the HPRP and ZA with exact and inexact line searches. The exact line search uses Newton’s method and quadratic interpolation is used for the inexact line search. The performance of each method on random test problems was evaluated by observing the number of iterations and time required to find the weighted analytic center. Our numerical methods indicate that ZA is better than HPRP with any of the two line searches, in terms of the number of iterations and time to find the weighted analytic center. Quadratic interpolation inexact line search gives the best success rate and fewest number of iterations for the CG methods considered. On the other hand, the fastest time for the CG methods is found with the Newton’s exact line search. In addition, these results indicate that for each of the methods, our Quadratic interpolation inexact line search has a higher cost per iteration than that of the Newton’s exact line search. VL - 10 IS - 6 ER -
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