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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...

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

Y. Q. Bai;  F. Y. Wang;  X. W. Luo — 2010

RAIRO - Operations Research

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.

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