| On KKT points of Celis-Dennis-Tapia subproblem |
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| 作者姓名： | LI Gaidi College of Applied Sciences Beijing University of Technology Beijing China |
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| 作者单位： | LI Gaidi College of Applied Sciences，Beijing University of Technology，Beijing 100022，China |
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| 摘 要： | The Celis-Dennis-Tapia(CDT) problem is a subproblem of the trust region algorithms for the constrained optimization. CDT subproblem is studied in this paper. It is shown that there exists the KKT point such that the Hessian matrix of the Lagrangian is positive semidefinite, if the multipliers at the global solution are not unique. Next the second order optimality conditions are also given, when the Hessian matrix of Lagrange at the solution has one negative eigenvalue. And furthermore, it is proved that all feasible KKT points satisfying that the corresponding Hessian matrices of Lagrange have one negative eigenvalue are the local optimal solutions of the CDT subproblem.
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| 收稿时间： | 13 March 2005 |
| 修稿时间： | 13 December 2005 |
On KKT points of Celis-Dennis-Tapia subproblem |
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| LI Gaidi College of Applied Sciences,Beijing University of Technology,Beijing ,China.On KKT points of Celis-Dennis-Tapia subproblem[J].Science in China(Mathematics),2006,49(5):651-659. |
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| Authors: | LI Gaidi |
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| Institution: | College of Applied Sciences, Beijing University of Technology, Beijing 100022, China |
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| Abstract: | The Celis-Dennis-Tapia(CDT) problem is a subproblem of the trust region algorithms for the constrained optimization. CDT subproblem is studied in this paper. It is shown that there exists the KKT point such that the Hessian matrix of the Lagrangian is positive semidefinite, if the multipliers at the global solution are not unique. Next the second order optimality conditions are also given, when the Hessian matrix of Lagrange at the solution has one negative eigenvalue. And furthermore, it is proved that all feasible KKT points satisfying that the corresponding Hessian matrices of Lagrange have one negative eigenvalue are the local optimal solutions of the CDT subproblem. |
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| Keywords: | CDT subproblem local solution optimality condition saddle point |
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