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Zbl 1170.90455
El Ghami, M.; Bai, Y.Q.; Roos, C.
Kernel-function based algorithms for semidefinite optimization. (English)
[J] RAIRO, Oper. Res. 43, No. 2, 189-199 (2009). ISSN 0399-0559; ISSN 1290-3868/e

Summary: Recently, the authors [SIAM J. Optim. 15, No.~1, 101--128 (2004; Zbl 1077.90038)] 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 analogous to the results in [loc. cit.] for LO.

MSC 2000:: *90C22 Semidefinite programming
90C31 Sensitivity, etc.

Keywords: interior-point methods; primal-dual method; complexity

Citations: Zbl 1077.90038

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