@article {8656,
	title = {Kernel function based interior point algorithms for linear optimisation},
	journal = {International Journal of Mathematical Modelling and Numerical Optimisation},
	volume = {9},
	number = {2},
	year = {2019},
	pages = {158 - 177},
	abstract = {We propose a primal-dual interior-point algorithm for linear optimisation based on a class of kernel functions which is eligible. New search directions and proximity measures are defined based on these functions. We derive the complexity bounds for large and small-update methods respectively. These are currently the best known complexity results for such methods.},
	url = {https://www.inderscience.com/info/inarticle.php?artid=98785},
	author = {El Amir Djeffal and Bachir Bounibane}
}
@article {8657,
	title = {A primal dual interior point method based on a new kernel function for linear complementarity problem},
	journal = {Asian-European Journal of Mathematics},
	year = {2018},
	abstract = {In this paper, we present an interior-point algorithm for solving an optimization problem using the central path method. By an equivalent reformulation of the central path, we obtain a new search direction which targets at a small neighborhood of the central path. For a full-Newton step interior-point algorithm based on this search direction, the complexity bound of the algorithm is the best known for linear complementarity problem. For its numerical tests, some strategies are used and indicate that the algorithm is efficient.},
	url = {https://doi.org/10.1142/S1793557120500011},
	author = {El Amir Djeffal and Mounia Laouar}
}
@inbook {8714,
	title = {New Complexity Analysis of the Path Following Method for Linear Complementarity Problem},
	booktitle = { Intelligent Mathematics II: Applied Mathematics and Approximation Theory},
	year = {2016},
	abstract = {In this paper, we present an interior point algorithm for solving an optimization problem using the central path method. By an equivalent reformulation of the central path, we obtain a new search direction which targets at a small neighborhood of the central path. For a full-Newton step interior-point algorithm based on this search direction, the complexity bound of the algorithm is the best known for linear complementarity problem. For its numerical tests some strategies are used and indicate that the algorithm is efficient.},
	url = {DOI: 10.1007/978-3-319-30322-2_6},
	author = {El Amir Djeffal and Lakhdar Djeffal and Farouk Benoumelaz}
}
@article {8713,
	title = {A path following interior-point algorithm for semidefinite optimization problem based on new kernel function},
	journal = {Journal of Mathematical Modeling},
	volume = {4},
	number = {1},
	year = {2016},
	pages = {35-58},
	abstract = {In this paper, we deal to obtain some new complexity results for solving semidefinite optimization (SDO) problem by interior-point methods (IPMs). We define a new proximity function for the SDO by a new kernel function. Furthermore we formulate an algorithm for a primal dual interior-point method (IPM) for the SDO by using the proximity function and give its complexity analysis, and then we show that the worst-case iteration bound for our IPM is\&nbsp;O(6(m+1)3m+42(m+1)Ψm+22(m+1)01θlognμ0ε)O(6(m+1)3m+42(m+1)Ψ0m+22(m+1)1θlog⁡nμ0ε), where\&nbsp;m\&gt;4m\&gt;4.},
	url = {https://jmm.guilan.ac.ir/?_action=article\&au=10070\&_au=El+Amir++Djeffal},
	author = {El Amir Djeffal and Lakhdar Djeffal}
}
@article {8715,
	title = {Feasible short-step interior point algorithm for linear complementarity problem based on kernel function},
	journal = {AMO - Advanced Modeling and Optimization},
	volume = {15},
	number = {2},
	year = {2013},
	pages = {157-172},
	abstract = {In this paper we deal with the study of the polynomial complexity analysis and numerical implementation for a short-step interior point algorithm for monotone linear complementarity problems (LCP) based on karnel function. The analysis is based on a new class of search directions. We establish the global convergence of the algorithm. Furthermore, it is shown that the algorithm has O(n 2.5L), iteration complexity. For its numerical tests some strategies are used and indicate that the algorithm is efficient.},
	url = {https://camo.ici.ro/journal/vol15/v15b3.pdf},
	author = {El Amir Djeffal and Lakhdar Djeffal}
}
