Abstract
A trust region method for the solution of nonlinear optimization problems with norm constraints is analyzed. Such optimization problems arise in parameter identification and nonlinear eigenvalue problems. The characteristics of these applications motivate the formulation and analysis of the trust region method. The algorithms studied here allow for inexact gradient information and the use of subspace methods for the approximate solution of subproblems. Characterizations and the descent properties of trust region steps are given, criteria for the existence of successful iterations under inexact gradient information and under the use of subspace methods are established, and global convergence of the method is proven.
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