Displaying similar documents to “A Polynomial-time Interior-point Algorithm for Convex Quadratic Semidefinite Optimization”

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...

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 1 6 when compared with the method based on the use of...

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...

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...

Nonmonotone strategy for minimization of quadratics with simple constraints

M. A. Diniz-Ehrhardt, Zdeněk Dostál, M. A. Gomes-Ruggiero, J. M. Martínez, Sandra Augusta Santos (2001)

Applications of Mathematics

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An algorithm for quadratic minimization with simple bounds is introduced, combining, as many well-known methods do, active set strategies and projection steps. The novelty is that here the criterion for acceptance of a projected trial point is weaker than the usual ones, which are based on monotone decrease of the objective function. It is proved that convergence follows as in the monotone case. Numerical experiments with bound-constrained quadratic problems from CUTE collection show...

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 ( 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.