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Kernel-function Based Algorithms for Semidefinite Optimization

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

RAIRO - Operations Research

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 are...

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

M. EL Ghami, T. Steihaug (2010)

RAIRO - Operations Research

Recently, [Y.Q. Bai, M. El Ghami and C. Roos, SIAM J. Opt. 15 (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 P*(κ) Linear Complementarity Problems (LCPs). The analysis for LCPs deviates significantly from the analysis for linear optimization....

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