Novel Kernel Function With a Hyperbolic Barrier Term to Primal-dual Interior Point Algorithm for SDP Problems

Touil, Imene; Chikouche, Wided

doi:10.1007/s10255-022-1061-0

Cited by 5 publications

(4 citation statements)

References 34 publications

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confidence: 85%

“…The following lemma provide an important feature of the hyperbolic cotangent function that enable us to prove the e-convexity of the new KF. Lemma 3.4 (Lemma 3.2 in [23]) Let ψ be the function defined in (1). Then, we have…”

Section: The New Kernel Function and Its Propertiesmentioning

confidence: 99%

“…See [9,24,6,10,12,16,11,26] for more informations on interior point algorithms based on KFs. It's worth noting that the latest type is the hyperbolic one which was recently introduced by Touil and Chikouche [22,23].…”

Section: Introductionmentioning

confidence: 99%

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A Primal-Dual Interior-Point Algorithm Based on a Kernel Function with a New Barrier Term

Guerdouh

Chikouche

Touil³

2023

Stat., optim. inf. comput.

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In this paper, we propose a path-following interior-point method (IPM) for solving linear optimization (LO) problems based on a new kernel function (KF). The latter differs from other KFs in having an exponential-hyperbolic barrier term that belongs to the hyperbolic type, recently developed by I. Touil and W. Chikouche \cite{filomat2021,acta2022}. The complexity analysis for large-update primal-dual IPMs based on this KF yields an $\mathcal{O}\left( \sqrt{n}\log^2n\log \frac{n}{\epsilon }\right)$ iteration bound which improves the classical iteration bound. For small-update methods, the proposed algorithm enjoys the favorable iteration bound, namely, $\mathcal{O}\left( \sqrt{n}\log \frac{n}{\epsilon }\right)$. We back up these results with some preliminary numerical tests which show that our algorithm outperformed other algorithms with better theoretical convergence complexity. To our knowledge, this is the first feasible primal-dual interior-point algorithm based on an exponential-hyperbolic KF.

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confidence: 85%

Section: The New Kernel Function and Its Propertiesmentioning

confidence: 99%

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A Primal-Dual Interior-Point Algorithm Based on a Kernel Function with a New Barrier Term

Guerdouh

Chikouche

Touil³

2023

Stat., optim. inf. comput.

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“…They proved that the corresponding interior-point algorithm meets O(n 2 3 log n ) iterations as the worst case complexity bound for the large-update method. In another paper [50], they presented an IPM based on a pure hyperbolic barrier term. By parametrizing the latter, Guerdouh et al in [29] improved the complexity bound for large-update IPMs from O(n 3 4 log n ) to the currently best one.…”

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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Spectrally efficient IR-UWB pulse designs based on linear combinations of Gaussian Derivatives

Taki

Abou-Rjeily

2022

Telecommun Syst

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Pulse design is critical for impulse radio communications, as it determines the transmission efficiency with respect to regulation spectral limits. In this paper, we propose the design of several novel pulse shapes relying on combinations of Gaussian derivatives with the target of improving the spectral efficiency. A general model for maximizing the efficiency of dual and triplet couplings is presented, employing the interior point global optimization algorithm. Then, the spectrum peak frequency is derived in closed form for any combination of two Gaussians with consecutive orders of derivation. The parameters controlling the time properties of the generated waveforms have been adequately adjusted to reach the best compliance with the spectral mask. Novel pulses have been investigated providing a high efficiency using simple generation mechanisms, which can be practically implemented via analog circuits. Results demonstrated the advantage of the proposed pulse shapes in terms of the bit error rate performance for 2 Gbps OOK and 1 Gbps PPM in AWGN and multipath channels.

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Novel Kernel Function With a Hyperbolic Barrier Term to Primal-dual Interior Point Algorithm for SDP Problems

Cited by 5 publications

References 34 publications

A Primal-Dual Interior-Point Algorithm Based on a Kernel Function with a New Barrier Term

A Primal-Dual Interior-Point Algorithm Based on a Kernel Function with a New Barrier Term

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

Spectrally efficient IR-UWB pulse designs based on linear combinations of Gaussian Derivatives

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