Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems
Based on an inverse function theorem for a system of semismooth equations, this paper establishes several necessary and sufficient conditions for an isolated solution of a complementarity problem defined on the cone of symmetric positive semidefinite matrices to be strongly regular/stable. We show f...
| Main Authors: | , , |
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| Format: | Journal Article |
| Language: | English |
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Institute for Operations Research and the Management Sciences (I N F O R M S)
2003
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| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/91450 |
| _version_ | 1848765523941130240 |
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| author | Pang, J.S. Sun, D. Sun, Jie |
| author_facet | Pang, J.S. Sun, D. Sun, Jie |
| author_sort | Pang, J.S. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Based on an inverse function theorem for a system of semismooth equations, this paper establishes several necessary and sufficient conditions for an isolated solution of a complementarity problem defined on the cone of symmetric positive semidefinite matrices to be strongly regular/stable. We show further that for a parametric complementarity problem of this kind, if a solution corresponding to a base parameter is strongly stable, then a semismooth implicit solution function exists whose directional derivatives can be computed by solving certain affine problems on the critical cone at the base solution. Similar results are also derived for a complementarity problem defined on the Lorentz cone. The analysis relies on some new properties of the directional derivatives of the projector onto the semidefinite cone and the Lorentz cone. |
| first_indexed | 2025-11-14T11:36:37Z |
| format | Journal Article |
| id | curtin-20.500.11937-91450 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T11:36:37Z |
| publishDate | 2003 |
| publisher | Institute for Operations Research and the Management Sciences (I N F O R M S) |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-914502023-04-20T04:48:11Z Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems Pang, J.S. Sun, D. Sun, Jie Science & Technology Technology Physical Sciences Operations Research & Management Science Mathematics, Applied Mathematics complementarity problem variational inequality semidefinite cone Lorentz cone IMPLICIT-FUNCTION THEOREM VARIATIONAL-INEQUALITIES NEWTON METHOD SENSITIVITY-ANALYSIS METRIC PROJECTIONS NORMAL MAPS EQUATIONS DIFFERENTIABILITY OPTIMIZATION PROGRAMS Based on an inverse function theorem for a system of semismooth equations, this paper establishes several necessary and sufficient conditions for an isolated solution of a complementarity problem defined on the cone of symmetric positive semidefinite matrices to be strongly regular/stable. We show further that for a parametric complementarity problem of this kind, if a solution corresponding to a base parameter is strongly stable, then a semismooth implicit solution function exists whose directional derivatives can be computed by solving certain affine problems on the critical cone at the base solution. Similar results are also derived for a complementarity problem defined on the Lorentz cone. The analysis relies on some new properties of the directional derivatives of the projector onto the semidefinite cone and the Lorentz cone. 2003 Journal Article http://hdl.handle.net/20.500.11937/91450 10.1287/moor.28.1.39.14258 English Institute for Operations Research and the Management Sciences (I N F O R M S) fulltext |
| spellingShingle | Science & Technology Technology Physical Sciences Operations Research & Management Science Mathematics, Applied Mathematics complementarity problem variational inequality semidefinite cone Lorentz cone IMPLICIT-FUNCTION THEOREM VARIATIONAL-INEQUALITIES NEWTON METHOD SENSITIVITY-ANALYSIS METRIC PROJECTIONS NORMAL MAPS EQUATIONS DIFFERENTIABILITY OPTIMIZATION PROGRAMS Pang, J.S. Sun, D. Sun, Jie Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems |
| title | Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems |
| title_full | Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems |
| title_fullStr | Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems |
| title_full_unstemmed | Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems |
| title_short | Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems |
| title_sort | semismooth homeomorphisms and strong stability of semidefinite and lorentz complementarity problems |
| topic | Science & Technology Technology Physical Sciences Operations Research & Management Science Mathematics, Applied Mathematics complementarity problem variational inequality semidefinite cone Lorentz cone IMPLICIT-FUNCTION THEOREM VARIATIONAL-INEQUALITIES NEWTON METHOD SENSITIVITY-ANALYSIS METRIC PROJECTIONS NORMAL MAPS EQUATIONS DIFFERENTIABILITY OPTIMIZATION PROGRAMS |
| url | http://hdl.handle.net/20.500.11937/91450 |