A Regularized Smoothing Newton Method for Symmetric Cone Complementarity Problems

This paper extends the regularized smoothing Newton method in vector complementarity problems to symmetric cone complementarity problems (SCCP), which includes the nonlinear complementarity problem, the second-order cone complementarity problem, and the semidefinite complementarity problem as specia...

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Bibliographic Details
Published in:SIAM journal on optimization 2008-01, Vol.19 (3), p.1028-1047
Main Authors: Kong, Lingchen, Sun, Jie, Xiu, Naihua
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Applied mathematics
Approximation
Euclidean space
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Summary:This paper extends the regularized smoothing Newton method in vector complementarity problems to symmetric cone complementarity problems (SCCP), which includes the nonlinear complementarity problem, the second-order cone complementarity problem, and the semidefinite complementarity problem as special cases. In particular, we study strong semismoothness and Jacobian nonsingularity of the total natural residual function for SCCP. We also derive the uniform approximation property and the Jacobian consistency of the Chen-Mangasarian smoothing function of the natural residual. Based on these properties, global and quadratical convergence of the proposed algorithm is established.
ISSN:1052-6234
1095-7189
DOI:10.1137/060676775