NONLINEAR PERTURBATIONS OF POLYHEDRAL NORMAL CONE MAPPINGS AND AFFINE VARIATIONAL INEQUALITIES
This paper establishes an upper estimate for the Frechet normal cone to the graph of the nonlinearly perturbed polyhedral normal cone mappings in finite dimensional spaces. Under a positive linear independence assumption on the normal vectors of the active constraints at the point in question, the r...
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| Format: | Article |
| Language: | English |
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Dalat University
2012-09-01
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| Series: | Tạp chí Khoa học Đại học Đà Lạt |
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| Online Access: | https://tckh.dlu.edu.vn/index.php/tckhdhdl/article/view/208 |
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| _version_ | 1832572080882712576 |
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| author | Nguyễn Thành Quí |
| author_facet | Nguyễn Thành Quí |
| author_sort | Nguyễn Thành Quí |
| collection | DOAJ |
| description | This paper establishes an upper estimate for the Frechet normal cone to the graph of the nonlinearly perturbed polyhedral normal cone mappings in finite dimensional spaces. Under a positive linear independence assumption on the normal vectors of the active constraints at the point in question, the result leads to an upper estimate for values of the Mordukhovich coderivative of such mappings. On the basis, new results on solution stability of parametric affine variational inequalities under nonlinear perturbations are derived. |
| format | Article |
| id | doaj-art-877f17ab22454bcba237d867a7bead29 |
| institution | Kabale University |
| issn | 0866-787X |
| language | English |
| publishDate | 2012-09-01 |
| publisher | Dalat University |
| record_format | Article |
| series | Tạp chí Khoa học Đại học Đà Lạt |
| spelling | doaj-art-877f17ab22454bcba237d867a7bead292025-02-02T12:00:52ZengDalat UniversityTạp chí Khoa học Đại học Đà Lạt0866-787X2012-09-012310.37569/DalatUniversity.2.3.208(2012)NONLINEAR PERTURBATIONS OF POLYHEDRAL NORMAL CONE MAPPINGS AND AFFINE VARIATIONAL INEQUALITIESNguyễn Thành Quí0College of Information and Communication Technology, Cantho UniversityThis paper establishes an upper estimate for the Frechet normal cone to the graph of the nonlinearly perturbed polyhedral normal cone mappings in finite dimensional spaces. Under a positive linear independence assumption on the normal vectors of the active constraints at the point in question, the result leads to an upper estimate for values of the Mordukhovich coderivative of such mappings. On the basis, new results on solution stability of parametric affine variational inequalities under nonlinear perturbations are derived.https://tckh.dlu.edu.vn/index.php/tckhdhdl/article/view/208Polyhedral normal cone mappingNonlinear perturbationFrechet normal coneLimiting normal coneMordukhovich coderivativeEstimate |
| spellingShingle | Nguyễn Thành Quí NONLINEAR PERTURBATIONS OF POLYHEDRAL NORMAL CONE MAPPINGS AND AFFINE VARIATIONAL INEQUALITIES Tạp chí Khoa học Đại học Đà Lạt Polyhedral normal cone mapping Nonlinear perturbation Frechet normal cone Limiting normal cone Mordukhovich coderivative Estimate |
| title | NONLINEAR PERTURBATIONS OF POLYHEDRAL NORMAL CONE MAPPINGS AND AFFINE VARIATIONAL INEQUALITIES |
| title_full | NONLINEAR PERTURBATIONS OF POLYHEDRAL NORMAL CONE MAPPINGS AND AFFINE VARIATIONAL INEQUALITIES |
| title_fullStr | NONLINEAR PERTURBATIONS OF POLYHEDRAL NORMAL CONE MAPPINGS AND AFFINE VARIATIONAL INEQUALITIES |
| title_full_unstemmed | NONLINEAR PERTURBATIONS OF POLYHEDRAL NORMAL CONE MAPPINGS AND AFFINE VARIATIONAL INEQUALITIES |
| title_short | NONLINEAR PERTURBATIONS OF POLYHEDRAL NORMAL CONE MAPPINGS AND AFFINE VARIATIONAL INEQUALITIES |
| title_sort | nonlinear perturbations of polyhedral normal cone mappings and affine variational inequalities |
| topic | Polyhedral normal cone mapping Nonlinear perturbation Frechet normal cone Limiting normal cone Mordukhovich coderivative Estimate |
| url | https://tckh.dlu.edu.vn/index.php/tckhdhdl/article/view/208 |
| work_keys_str_mv | AT nguyenthanhqui nonlinearperturbationsofpolyhedralnormalconemappingsandaffinevariationalinequalities |