Displaying similar documents to “Generic Primal-dual Interior Point Methods Based on a New Kernel Function”

Kernel-function Based Primal-Dual Algorithms for () Linear Complementarity Problems

M. EL Ghami, T. Steihaug (2010)

RAIRO - Operations Research

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Recently, [Y.Q. Bai, M. El Ghami and C. Roos, SIAM J. Opt. (2004) 101–128] investigated a new class of kernel functions which differs from the class of self-regular kernel functions. The class is defined by some simple conditions on the growth and the barrier behavior of the kernel function. In this paper we generalize the analysis presented in the above paper for () Linear Complementarity Problems (LCPs). The analysis for LCPs deviates significantly from the analysis for...

A Polynomial-time Interior-point Algorithm for Convex Quadratic Semidefinite Optimization

Y. Q. Bai, F. Y. Wang, X. W. Luo (2010)

RAIRO - Operations Research

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In this paper we propose a primal-dual interior-point algorithm for convex quadratic semidefinite optimization problem. The search direction of algorithm is defined in terms of a matrix function and the iteration is generated by full-Newton step. Furthermore, we derive the iteration bound for the algorithm with small-update method, namely, ( n log n ε ), which is best-known bound so far.

Kernel-function Based Algorithms for Semidefinite Optimization

M. EL Ghami, Y. Q. Bai, C. Roos (2009)

RAIRO - Operations Research

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Recently, Y.Q. Bai, M. El Ghami and C. Roos [3] introduced a new class of so-called eligible kernel functions which are defined by some simple conditions. The authors designed primal-dual interior-point methods for linear optimization (LO) based on eligible kernel functions and simplified the analysis of these methods considerably. In this paper we consider the semidefinite optimization (SDO) problem and we generalize the aforementioned results for LO to SDO. The iteration bounds obtained...

An adaptive long step interior point algorithm for linear optimization

Maziar Salahi (2010)

Kybernetika

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It is well known that a large neighborhood interior point algorithm for linear optimization performs much better in implementation than its small neighborhood counterparts. One of the key elements of interior point algorithms is how to update the barrier parameter. The main goal of this paper is to introduce an “adaptive” long step interior-point algorithm in a large neighborhood of central path using the classical logarithmic barrier function having O ( n log ( x 0 ) T s 0 ϵ ) iteration complexity analogous...

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 (2023)

Kybernetika

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In this paper, we first present a polynomial-time primal-dual interior-point method (IPM) for solving linear programming (LP) problems, based on a new kernel function (KF) with a hyperbolic-logarithmic barrier term. To improve the iteration bound, we propose a parameterized version of this function. We show that the complexity result meets the currently best iteration bound for large-update methods by choosing a special value of the parameter. Numerical experiments reveal that the new...