A smoothing-type algorithm for the second-order cone complementarity problem with a new nonmonotone line search

Abstract

The second-order cone complementarity problem (denoted by SOCCP) can be effectively solved by smoothing-type algorithms, which in general are designed based on some monotone line search. In this paper, based on a new smoothing function of the Fischer–Burmeister function, we propose a smoothing-type algorithm for solving the SOCCP. The proposed algorithm uses a new nonmonotone line search scheme, which contains the usual monotone line search as a special case. Under suitable assumptions, we show that the proposed algorithm is globally and locally quadratically convergent. Some numerical results are reported which indicate the effectiveness of the proposed algorithm.

Keywords:

• second-order cone complementarity problem
• smoothing Newton method
• nonmonotone line search
• convergence

AMS Subject Classifications:

• 90C33
• 65K05

Acknowledgments

The authors are grateful to the referees for their careful reading and helpful suggestions that improved the paper greatly.

Notes

1 This paper was partly supported by National Natural Science Foundation of China [grant number 11101248], [grant number 11371306]; Research Award Foundation for Outstanding Young Scientists of Shandong Province [grant number BS2012SF025] and Science Technology Research Projects of Education Department of Henan Province [grant number 13A110767].