Uniform nonsingularity and complementarity problems over symmetric cones

Abstract. We study the uniform nonsingularity property recently proposed by the authors and present its applications to nonlinear complementarity problems over a symmetric cone. In particular, by addressing theoretical issues such as the existence of Newton directions, the boundedness of iterates and the nonsingularity of B-subdifferentials, we show that the non-interior continuation method proposed by Xin Chen and Paul Tseng and the squared smoothing Newton method proposed by Liqun Qi, Defeng Sun and Jie Sun are applicable to a more general class of nonmonotone problems. Interestingly, we also show that the linear complementarity problem is globally uniquely solvable under the assumption of uniform nonsingularity.