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Optimality conditions for cdt subproblem (1997).
| Content Provider | CiteSeerX |
|---|---|
| Author | Chen, Xiongda Yuan, Yaxiang |
| Abstract | : In this paper, we give necessary and sufficient optimality conditions which are easy verified for the local solution of Celis-Dennis-Tapia subproblem (CDT subproblem) where the Hessian at this local solution has one negative eigenvalue. If CDT subproblem has no global solution with Hessian of Lagrangian positive semi-definite, the Hessian of Lagrangian has at least one negative eigenvalue. It is very important to investigate all the stationary points of Lagrangian dual function and to characterize the local solutions. We also discuss the gap between these two conditions. Key Words: CDT subproblem, optimality condition. 1 INTRODUCTION The CDT subproblem is proposed by Celis, Dennis and Tapia (1985) in order to overcome the difficulty of inconsistency when one applies the sequence quadratic programming method with the trust region for the constrained optimization, for example, see Powell and Yuan (1991). The CDT subproblem has the following form: min d2R n \Phi(d) = 1 2 d T Bd ... |
| File Format | |
| Publisher Date | 1997-01-01 |
| Access Restriction | Open |
| Subject Keyword | Cdt Subproblem Optimality Condition Local Solution Negative Eigenvalue Sequence Quadratic Programming Method Lagrangian Positive Semi-definite Global Solution Sufficient Optimality Condition Celis-dennis-tapia Subproblem Lagrangian Dual Function Following Form Stationary Point Trust Region Constrained Optimization Key Word Min D2r Phi |
| Content Type | Text |
