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

Safa Guerdouh; Wided Chikouche; Imene Touil; Adnan Yassine

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Displaying similar documents to “Complexity of primal-dual interior-point algorithm for linear programming based on a new class of kernel functions”

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

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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 $O (\sqrt{n} log (n) log (\frac{n}{ε}))$ for large-update algorithm with the special choice of its parameter $m$ and thus improves the iteration bound obtained in Bai et al. [] for large-update algorithm. ...

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CONTENTS1. Introduction..................................................................................................................................... 5 1.1. Main Theorem 1.1................................................................................................................. 8 1.2. Main Theorem 1.2................................................................................................................. 92. Radon transform.......................................................................................................................................

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We propose a feasible primal-dual path-following interior-point algorithm for semidefinite least squares problems (SDLS). At each iteration, the algorithm uses only full Nesterov-Todd steps with the advantage that no line search is required. Under new appropriate choices of the parameter $β$ which defines the size of the neighborhood of the central-path and of the parameter $θ$ which determines the rate of decrease of the barrier parameter, we show that the proposed algorithm is well defined...

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Let $G \subset 𝐒𝐔 (2, 1)$ be a non-elementary complex hyperbolic Kleinian group. If $G$ preserves a complex line, then $G$ is $ℂ$ -Fuchsian; if $G$ preserves a Lagrangian plane, then $G$ is $ℝ$ -Fuchsian; $G$ is Fuchsian if $G$ is either $ℂ$ -Fuchsian or $ℝ$ -Fuchsian. In this paper, we prove that if the traces of all elements in $G$ are real, then $G$ is Fuchsian. This is an analogous result of Theorem V.G. 18 of B. Maskit, Kleinian Groups, Springer-Verlag, Berlin, 1988, in the setting of complex hyperbolic isometric groups. As an...

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Distributed dual averaging algorithm for multi-agent optimization with coupled constraints

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