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