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

ABSTRACT

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].

KEYWORDS:

• Homogeneous algorithm
• nonlinear complementarity problem
• complexity
• interior point algorithm
• symmetric cone

AMS SUBJECT CLASSIFICATIONS:

• 90C33
• 90C51
• 90C25

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work supported by the Natural Science Foundation of Shaanxi Province of China under Grant 2017JM1014; the funding of Xianyang Normal University under Grant XSYK17015.