On Local Solutions of the Celis--Dennis--Tapia Subproblem

Authors:
Xiongda Chen;Ya-xiang Yuan
Affiliations:
-;-
Venue:
SIAM Journal on Optimization
Year:
1999

Citing 0
Cited 2

The convergence of subspace trust region methods

Journal of Computational and Applied Mathematics
Regularized Lagrangian duality for linearly constrained quadratic optimization and trust-region problems

Journal of Global Optimization

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Abstract

We discuss the distribution of the local solutions of the Celis--Dennis--Tapia (CDT) subproblem, which appears in some trust region algorithms for nonlinear optimization. We also give some examples to show the differences between the CDT subproblem and the single-ball-constraint subproblem. These results show that the complexity of the CDT subproblem does not depend on the complexity of the structure of the dual plane. Thus they provide the possibility to search for the global minimizer in the dual plane.