ON CONVERGENCE IN DISCRETIZED MINIMIZATION PROBLEMS*
Rolf Dieter Grigorieff · Numerical Functional Analysis and Optimization · 2001
Let a norm minimisation problem be given, where the minimisation takes place over the range of an in general nonlinear map. The given problem is approximated by a sequence of similar but finite dimensional minimisation problems. The convergence of the infima and the approximate solutions is studied in an abstract setting. As a special case general minimisation problems of functionals are included. Application of the abstract results are presented to nonlinear Chebyshev approximation, nonlinear approximation problems in Lp -spaces, a nonlinear defect minimisation problem for an elliptic boundary value problem and a minimisation problem for a convex functional in L ∞. The paper partially extends earlier joint work by R. Reemtsen and the author. *Dedicated to Friedrich Stummel on the occasion of his 70th birthday.