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...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
Society for Industrial and Applied Mathematics
2008
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| Online Access: | http://hdl.handle.net/20.500.11937/46475 |
| _version_ | 1848757568246120448 |
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| author | Kong, L. Sun, Jie Xiu, N. |
| author_facet | Kong, L. Sun, Jie Xiu, N. |
| author_sort | Kong, L. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T09:30:10Z |
| format | Journal Article |
| id | curtin-20.500.11937-46475 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:30:10Z |
| publishDate | 2008 |
| publisher | Society for Industrial and Applied Mathematics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-464752017-09-13T13:39:37Z A regularized smoothing Newton method for symmetric cone complementarity problems Kong, L. Sun, Jie Xiu, N. 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. 2008 Journal Article http://hdl.handle.net/20.500.11937/46475 10.1137/060676775 Society for Industrial and Applied Mathematics fulltext |
| spellingShingle | Kong, L. Sun, Jie Xiu, N. A regularized smoothing Newton method for symmetric cone complementarity problems |
| title | A regularized smoothing Newton method for symmetric cone complementarity problems |
| title_full | A regularized smoothing Newton method for symmetric cone complementarity problems |
| title_fullStr | A regularized smoothing Newton method for symmetric cone complementarity problems |
| title_full_unstemmed | A regularized smoothing Newton method for symmetric cone complementarity problems |
| title_short | A regularized smoothing Newton method for symmetric cone complementarity problems |
| title_sort | regularized smoothing newton method for symmetric cone complementarity problems |
| url | http://hdl.handle.net/20.500.11937/46475 |