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.
Citation
Research report, School of Physical and Mathematical Sciences, Nanyang Technological Unversity, Singapore, July 2009