A polynomial-time algorithm for linear optimization based on a new kernel function with trigonometric barrier term

Kheirfam, Behrouz; Moslemi, M.

doi:10.2298/yjor120904006k

Cited by 12 publications

(3 citation statements)

References 17 publications

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“…We cannot talk about KFs without mentioning trigonometric KFs. This type of functions has been extensively explored in the literature [14,30,31,34,36,38,44], starting with the work of El Ghami et al [25] where the authors studied an IPM based on the first trigonometric KF introduced in [6]. They established that the complexity bounds for large-and small-update methods are O(n 3 4 log n ) and O( √ n log n ) respectively.…”

Section: Introductionmentioning

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: Introductionmentioning

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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“…Bai et al [1] presented a large class of eligible kernel functions, which is fairly general and includes the classical logarithmic functions and the self-regular functions, as well as many non-self-regular functions as special cases. For some other related kernel function, we refer to [3,4,5,6,7,8,9,12].…”

Section: Introductionmentioning

confidence: 99%

Complexity analysis of interior point methods for convex quadratic programming based on a parameterized Kernel function

Boudjellal

Roumili

Benterki

2022

bspm

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The kernel functions play an important role in the amelioration of the computational complexity of algorithms. In this paper, we present a primal-dual interior-point algorithm for solving convex quadratic programming based on a new parametric kernel function. The proposed kernel function is not logarithmic and not self-regular. We analysis a large and small-update versions which are based on a new kernel function. We obtain the best known iteration bound for large-update methods, which improves signicantly the so far obtained complexity results. Thisresult is the rst to reach this goal.

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“…In this sense, Bai et al [4] presented a large class of eligible kernel functions, which is fairly general and includes the classical logarithmic functions and the self-regular functions, as well as many non-self-regular functions as special cases. For some other related kernel function, we refer to [5][6][7]13,21,22,24].…”

mentioning

confidence: 99%

Interior-point algorithm for linear programming based on a new descent direction

Billel,

Djamel,

Aicha

et al. 2023

RAIRO-Oper. Res.

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We present a full-Newton step feasible interior-point algorithm for linear optimization based on a new search direction. We apply a vector-valued function generated by a univariate function on a new type of transformation on the centering equations of the system which characterizes the central path. For this, we consider a new function ψ(t) = t7\4. Furthermore, we show that the algorithm finds the ϵ-optimal solution of the underlying problem in polynomial time, namely O(√nlog(n+3\7√2)) iterations. Finally, a comparative numerical study is reported in order to analyze the efficiency of the proposed algorithm.

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A polynomial-time algorithm for linear optimization based on a new kernel function with trigonometric barrier term

Cited by 12 publications

References 17 publications

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

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

Complexity analysis of interior point methods for convex quadratic programming based on a parameterized Kernel function

Interior-point algorithm for linear programming based on a new descent direction

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