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 linear...
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
when compared with the method based on the use of the
classical...
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...
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