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

M. EL Ghami; T. Steihaug

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Displaying similar documents to “Kernel-function Based Primal-Dual Algorithms for P*(κ) Linear Complementarity Problems”

Generic Primal-dual Interior Point Methods Based on a New Kernel Function

M. EL Ghami, C. Roos (2008)

RAIRO - Operations Research

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In this paper we present a generic primal-dual interior point methods (IPMs) for linear optimization in which the search direction depends on a univariate kernel function which is also used as proximity measure in the analysis of the algorithm. The proposed kernel function does not satisfy all the conditions proposed in [2]. We show that the corresponding large-update algorithm improves the iteration complexity with a factor $n^{\frac{1}{6}}$ when compared with the method based on the use of...

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...

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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, ( $\sqrt{n}$ log $\frac{n}{ε}$ ), which is best-known bound so far.

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 $O (n log \frac{{(x^{0})}^{T} s^{0}}{ϵ})$ iteration complexity analogous...

An interior point algorithm for convex quadratic programming with strict equilibrium constraints

Rachid Benouahboun, Abdelatif Mansouri (2005)

RAIRO - Operations Research - Recherche Opérationnelle

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We describe an interior point algorithm for convex quadratic problem with a strict complementarity constraints. We show that under some assumptions the approach requires a total of $O (\sqrt{n} L)$ number of iterations, where $L$ is the input size of the problem. The algorithm generates a sequence of problems, each of which is approximately solved by Newton’s method.

A Primal-Dual Exterior Point Algorithm for Linear Programming Problems

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Large deviations for one dimensional diffusions with a strong drift.

Voss, Jochen (2008)

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