On KKT points of Celis-Dennis-Tapia subproblem  

作　　者：LI Gaidi 

机构地区：[1]College of Applied Sciences, Beijing University of Technology, Beijing 100022, China

出　　处：《Science China Mathematics》2006年第5期651-659,共9页中国科学：数学（英文版）

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).

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.

关 键 词：CDT subproblem  LOCAL solution  OPTIMALITY condition  SADDLE point. 

分 类 号：N[自然科学总论]