Interior-point methods for linear optimization based on a kernel function with a trigonometric barrier term

Ghami, Mohamed El; Guennoun, Zouhair; Bouali, S.; Steihaug, Trond

doi:10.1016/j.cam.2011.05.036

Cited by 60 publications

(53 citation statements)

References 8 publications

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“…which is exactly the same inequality as Lemma 3.1 in [7]. This means that our analysis closely resembles the analysis of the LO case in [7].…”

Section: The Decrease Of the Proximity In The Inner Iterationsupporting

confidence: 77%

“…This means that our analysis closely resembles the analysis of the LO case in [7]. From this stage on we can apply similar arguments as in the LO case.…”

Section: The Decrease Of the Proximity In The Inner Iterationsupporting

confidence: 68%

“…The extension to P * (κ)-linear complementarity problem was also presented in [10]. The obtained complexity for large-update improve significantly the complexity obtained in [6,7]. In this paper we consider kernel functions of the form…”

Section: Our Kernel Function and Some Of Its Propertiesmentioning

confidence: 92%

“…In the sequel we describe how the usual search directions are obtained for primal-dual methods for solving SDO problems. Our aim is to show that the kernel-function-based approach that we presented for LO in [7] can be generalized and applied also to SDO problems.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Primal-Dual Algorithms for Semidefinit Optimization Problems Based on Generalized Trigonometric Barrier Function

Ghami¹

2017

Int. J. of Pure and Appl. Math.

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Recently, M. Bouafoa, et al. [5] (Journal of optimization Theory and Applications, August, 2016),investigated a new kernel function which differs from the self-regular kernel functions. The kernel function has a trigonometric Barrier Term. In this paper we generalize the analysis presented in the above paper for Semidefinit Optimization Problems (SDO). It is shown that the interior-point methods based on this function for large-update methods, the iteration bound is improved significantly. For small-update interior point methods the iteration bound is the best currently known bound for primal-dual interior point methods. The analysis for SDO deviates significantly from the analysis for linear optimization. Several new tools and techniques are derived in this paper.

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“…which is exactly the same inequality as Lemma 3.1 in [7]. This means that our analysis closely resembles the analysis of the LO case in [7].…”

Section: The Decrease Of the Proximity In The Inner Iterationsupporting

confidence: 77%

“…This means that our analysis closely resembles the analysis of the LO case in [7]. From this stage on we can apply similar arguments as in the LO case.…”

Section: The Decrease Of the Proximity In The Inner Iterationsupporting

confidence: 68%

Section: Our Kernel Function and Some Of Its Propertiesmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Primal-Dual Algorithms for Semidefinit Optimization Problems Based on Generalized Trigonometric Barrier Function

Ghami¹

2017

Int. J. of Pure and Appl. Math.

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“…Peng et al [16] introduced self-regular barrier functions for primal-dual interior-point methods (IP M s) for LO, semidefinite optimization (SDO), second order cone optimization (SOCO) and also extended to P * (κ) LCP s. Recently in [2,7] the authors proposed a new primal-dual IP M for LO based on a new class of kernel functions which are not logarithmic and not necessarily self-regular barrier functions.…”

Section: Introductionmentioning

confidence: 99%

INTERIOR-POINT METHODS FOR $P_{*}(\kappa)$-LINEAR COMPLEMENTARITY PROBLEM BASED ON GENERALIZED TRIGONOMETRIC BARRIER FUNCTION

Ghami¹,

Wang²

2017

Int. J. of Appl. Math.

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Recently, M. Bouafoa, et al. [3] investigated a new kernel function which differs from the self-regular kernel functions. The kernel function has a trigonometric Barrier Term. In this paper we generalize the analysis presented in the above paper for P * (κ) Linear Complementarity Problems (LCPs). It is shown that the iteration bound for primal-dual large-update and small-update interior-point methods based on this function is as good as the currently best known iteration bounds for these type methods. The analysis for LCPs deviates significantly from the analysis for linear optimization. Several new tools and techniques are derived in this paper.

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Primal-Dual Algorithms for P ∗(κ) Linear Complementarity Problems Based on Kernel-Function with Trigonometric Barrier Term

Ghami¹

2012

Optimization Theory, Decision Making, and Operations Research Applications

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Interior-point methods for linear optimization based on a kernel function with a trigonometric barrier term

Cited by 60 publications

References 8 publications

Primal-Dual Algorithms for Semidefinit Optimization Problems Based on Generalized Trigonometric Barrier Function

Primal-Dual Algorithms for Semidefinit Optimization Problems Based on Generalized Trigonometric Barrier Function

INTERIOR-POINT METHODS FOR $P_{*}(\kappa)$-LINEAR COMPLEMENTARITY PROBLEM BASED ON GENERALIZED TRIGONOMETRIC BARRIER FUNCTION

Primal-Dual Algorithms for P ∗(κ) Linear Complementarity Problems Based on Kernel-Function with Trigonometric Barrier Term

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