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.
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.
基金
supported by the startup grants for doctoral research and the school grants for mathematical research of Beijing University of Technology
the National Natural Science Foundation of China(Grant No.10401038).
