Iterative complexities of a class of homogeneous algorithms for monotone nonlinear complementarity problems over symmetric cones.

This paper provides an analysis of the iterative complexities of a class of homogeneous algorithms for monotone nonlinear complementarity problems over symmetric cones. The proof of the complexity bounds requires that the nonlinear transformation satisfies an SLC. To prove the complexity bounds of the homogeneous algorithm, this paper proposes an SLC which does not depend on the scaling parameter p and is very easy to be verified. More important, it has scaled invariance. Underlying SLC, the obtained complexity bounds of the short-step algorithm, the semi-long-step algorithm and the long-step algorithm with the sx-direction match that of the homogeneous algorithms proposed by Yoshise [Homogenous algorithms for monotone complementarity problems over symmetric cones. Pac J Optim. 2008; 5(2):313-337]. [ABSTRACT FROM AUTHOR]