A full-Newton step infeasible interior-point algorithm based on a kernel function with a new barrier term

Guerdouh, Safa; Chikouche, Wided; Kheirfam, Behrouz

doi:10.1007/s12190-023-01858-8

Cited by 3 publications

(1 citation statement)

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“…As a further research we would like to extend our approach to more general optimization problems. Another question of interest is whether the new KF can be used to design an efficient infeasible interior-point algorithm as in [27,35,47].…”

Section: Conclusion and Remarksmentioning

confidence: 99%

Complexity of primal-dual interior-point algorithm for linear programming based on a new class of kernel functions

Guerdouh,

Chikouche,

Touil

et al. 2024

Kybernetika

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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 hyperboliclogarithmic 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.

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Section: Conclusion and Remarksmentioning

confidence: 99%