Mesh Independence for Nonlinear Least Squares Problems with Norm Constraints
If one solves an infinite dimensional optimization problem by introducing discretizations and applying a solution method to the resulting finite dimensional problem, one often observes a very stable behavior of this method with respect to varying discretizations. The most striking observation is the constancy of the number of iterations needed to satisfy a certain stopping criteria. In this paper we give give an analysis of this phenomena, the so called mesh independence, for nonlinear least squares problems with norm constraints (NCNLLS). A Gauss-Newton method for the solution of NCNLLS is discussed and a convergence theorem is given. The mesh independence is proven in its sharpest formulation. Sufficient conditions for the mesh independence to hold are related to conditions guaranteeing convergence of the Gauss-Newton method. The results are demonstrated on a two point boundary value problem.
Citable link to this pagehttps://hdl.handle.net/1911/101683
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