A Lipschitzian error bound for monotone symmetric cone linear complementarity problem

Abstract

We first discuss some properties of the solution set of a monotone symmetric cone linear complementarity problem (SCLCP), and then consider the limiting behaviour of a sequence of strictly feasible solutions within a wide neighbourhood of central trajectory for the monotone SCLCP. Under assumptions of strict complementarity and Slater’s condition, we provide four different characterizations of a Lipschitzian error bound for the monotone SCLCP in general Euclidean Jordan algebras. Thanks to the observation that a pair of primal-dual convex quadratic symmetric cone programming (CQSCP) problems can be exactly formulated as the monotone SCLCP, thus we obtain the same error bound results for CQSCP as a by-product.

Keywords:

• complementarity problem
• quadratic symmetric cone programming
• error bound

AMS Subject Classifications:

• 90C25
• 34A45
• 65G99

Acknowledgements

Both authors would like to thank Professor Oliver Stein for establishing the contact between them, and an anonymous referee for his careful reading. This paper is a revised version of a part of the corresponding author’s 2012 PhD dissertation at Nanyang Technological University, Singapore.

Notes

This research was partially supported by Scientific Research Foundation For Returned Scholars, Ministry of Education of China, the National Natural Science Foundations of China [grant number 11301080] and the project for nonlinear analysis and its applications [grant number IRTL1206].