| Title:
|
Complexity of primal-dual interior-point algorithm for linear programming based on a new class of kernel functions (English) |
| Author:
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Guerdouh, Safa |
| Author:
|
Chikouche, Wided |
| Author:
|
Touil, Imene |
| Author:
|
Yassine, Adnan |
| Language:
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English |
| Journal:
|
Kybernetika |
| ISSN:
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0023-5954 (print) |
| ISSN:
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1805-949X (online) |
| Volume:
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59 |
| Issue:
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6 |
| Year:
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2023 |
| Pages:
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827-860 |
| Summary lang:
|
English |
| . |
| Category:
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math |
| . |
| Summary:
|
In this paper, we first present a polynomial-time primal-dual interior-point method (IPM) for solving linear programming (LP) problems, based on a new kernel function (KF) with a hyperbolic-logarithmic barrier term. To improve the iteration bound, we propose a parameterized version of this function. We show that the complexity result meets the currently best iteration bound for large-update methods by choosing a special value of the parameter. Numerical experiments reveal that the new KFs have better results comparing with the existing KFs including $\log t$ in their barrier term. To the best of our knowledge, this is the first IPM based on a parameterized hyperbolic-logarithmic KF. Moreover, it contains the first hyperbolic-logarithmic KF (Touil and Chikouche in Filomat 34:3957-3969, 2020) as a special case up to a multiplicative constant, and improves significantly both its theoretical and practical results. (English) |
| Keyword:
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linear programming |
| Keyword:
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primal-dual interior-point methods |
| Keyword:
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kernel function |
| Keyword:
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complexity analysis |
| Keyword:
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large and small-update methods |
| MSC:
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90C05 |
| MSC:
|
90C51 |
| idZBL:
|
Zbl 07830567 |
| idMR:
|
MR4712965 |
| DOI:
|
10.14736/kyb-2023-6-0827 |
| . |
| Date available:
|
2024-02-26T11:09:50Z |
| Last updated:
|
2024-08-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152260 |
| . |
| Reference:
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