On local solutions of the Celis-Dennis-Tapia subproblem

We discuss the distribution of the local solutions of the Celis-Dennis-Tapi a (CDT) subproblem, which appears in some trust region algorithms for nonli near optimization. We also give some examples to show the differences betwe en the CDT subproblem and the single-ball-constraint subproblem. These resu lts show that the complexity of the CDT subproblem does not depend on the c omplexity of the structure of the dual plane. Thus they provide the possibi lity to search for the global minimizer in the dual plane.