An efficient parameterized logarithmic kernel function for linear optimization

Bouafia, Mousaab; Benterki, Djamel; Yassine, Adnan

doi:10.1007/s11590-017-1170-5

Cited by 13 publications

(7 citation statements)

References 14 publications

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“…Example 1. We consider the following (LO) problem (see [4]) n = 2k, A(i, j) = 0 if i = j and j = i + k 1 if i = j or j = i + k c(i) = −1, c(i + k) = 0, b(i) = 2, and the interior point condition (IPC), x 0 (i) = x 0 (i + k) = 1, y 0 (i) = −2, s 0 (i) = 1, s 0 (i + k) = 2 for i = 1, . .…”

Section: Numerical Resultsmentioning

confidence: 99%

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A new parameterized logarithmic kernel function for linear optimization with a double barrier term yielding the best known iteration bound

Ayache

Saoudi

2020

Communications in Mathematics

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In this paper, we propose a large-update primal-dual interior point algorithm for linear optimization. The method is based on a new class of kernel functions which differs from the existing kernel functions in which it has a double barrier term. The investigation according to it yields the best known iteration bound O( √ n log(n) log( n ε )) for large-update algorithm with the special choice of its parameter m and thus improves the iteration bound obtained in Bai et al. [2] for large-update algorithm. 2020 MSC: 90C05, 90C51, 90C31

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Section: Numerical Resultsmentioning

confidence: 99%

“…In 2018, Bouafia et al [4] proposed a parameterized logarithmic kernel function for primal-dual IPMs. They obtained the best known complexity results for large and small-update methods, they took the middle between Peng [9] and El Ghami's [6] barrier as a barrier term.…”

Section: Introductionmentioning

confidence: 99%

A new parameterized logarithmic kernel function for linear optimization with a double barrier term yielding the best known iteration bound

Ayache

Saoudi

2020

Communications in Mathematics

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“…Moreover, we improve the algorithmic complexity of the interior points method. We analyze large-update and small-update versions of the primal-dual interior algorithm described in Figure 1, which is based on the new parameterized kernel functions defined by (11). The results obtained in this paper represent important contributions to improve the convergence and the complexity analysis of primal-dual IPMs for LO.…”

Section: Discussionmentioning

confidence: 99%

An Effcient Primal-dual Interior Point Algorithm for Linear Optimization Problems Based an a New Parameterized Kernel Function With a Logarithmic Barrier Term

Djeffal

Boukhenchouche

2023

Preprint

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“…They are not only used for determining the search directions but also for measuring the distance between the given iterate and the µ-center for the algorithms. Currently, (IPMs) based on kernel function is one of the most effective methods for solving linear optimization problem (LO) and other convex optimization problems and is a very active research area in mathematical programming [1,2,4,5,6,7,9]. Recently in 2021, A. Bennani et al [3], is to solve (LFP) it by the projection method of interior points introduced by Ye-Lustig [15].…”

Section: Introductionmentioning

confidence: 99%

Extension of primal-dual interior point method based on a kernel function for linear fractional problem

Bouafia,

Yassine

2023

J. Numer. Anal. Approx. Theory

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Our aim in this work is to extend the primal-dual interior point method based on a kernel function for linear fractional problem. We apply the techniques of kernel function-based interior point methods to solve a standard linear fractional program. By relying on the method of Charnes and Cooper [3], we transform the standard linear fractional problem into a linear program. This transformation will allow us to define the associated linear program and solve it efficiently using an appropriate kernel function. To show the efficiency of our approach, we apply our algorithm on the standard linear fractional programming found in numerical tests in the paper of A. Bennani et al. [4], we introduce the linear programming associated with this problem. We give three interior point conditions on this example, which depend on the dimension of the problem. We give the optimal solution for each linear program and each linear fractional program. We also obtain, using the new algorithm, the optimal solutions for the previous two problems. Moreover, some numerical results are illustrated to show the effectiveness of the method.

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An efficient parameterized logarithmic kernel function for linear optimization

Cited by 13 publications

References 14 publications

A new parameterized logarithmic kernel function for linear optimization with a double barrier term yielding the best known iteration bound

A new parameterized logarithmic kernel function for linear optimization with a double barrier term yielding the best known iteration bound

An Effcient Primal-dual Interior Point Algorithm for Linear Optimization Problems Based an a New Parameterized Kernel Function With a Logarithmic Barrier Term

Extension of primal-dual interior point method based on a kernel function for linear fractional problem

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