An Efficient Primal–Dual Interior Point Method for Linear Programming Problems Based on a New Kernel Function with a Trigonometric Barrier Term

Bouafia, Mousaab; Benterki, Djamel; Yassine, Adnan

doi:10.1007/s10957-016-0895-0

Cited by 36 publications

(43 citation statements)

References 12 publications

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“…In this paper we extended the results obtained for kernel-function-based IPMs in [5] for LO to semidefinite optimization problems. The analysis in this paper is new and different from the one using for LO.…”

Section: Discussionmentioning

confidence: 88%

“…Having D X and D S , △X and △S can be calculated from (5). Due to the orthogonality of △X and △S, it is trivial to see that D X ⊥D S , and so…”

Section: New Search Directionmentioning

confidence: 99%

“…In general this will increase the value of Ψ(V ) above the threshold value τ . To get this value smaller again, and coming closer to the current µ-center, we solve the scaled search directions from (8), and unscale these directions by using (5). By choosing an appropriate step size α, we move along the search direction, and construct a new triple (X + , y + , S + ) with…”

Section: New Search Directionmentioning

confidence: 99%

“…Recently in [5] investigated new kernel functions with trigonometric barrier for linear optimization. The extension to P * (κ)-linear complementarity problem was also presented in [10].…”

Section: Our Kernel Function and Some Of Its Propertiesmentioning

confidence: 99%

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Abstract: 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.

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confidence: 99%

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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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Section: Discussionmentioning

confidence: 88%

“…Having D X and D S , △X and △S can be calculated from (5). Due to the orthogonality of △X and △S, it is trivial to see that D X ⊥D S , and so…”

Section: New Search Directionmentioning

confidence: 99%

Section: New Search Directionmentioning

confidence: 99%

“…Recently in [5] investigated new kernel functions with trigonometric barrier for linear optimization. The extension to P * (κ)-linear complementarity problem was also presented in [10].…”

Section: Our Kernel Function and Some Of Its Propertiesmentioning

confidence: 99%

“…

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mentioning

confidence: 99%

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