Titlebook: Ill-posed Variational Problems and Regularization Techniques; Proceedings of the “ Michel Théra,Rainer Tichatschke Conference proceedings 1

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,, Regularization of the Non-Parametric Minimal Surface Problem,er fairly general assumptions, we show that the approximate solutions (..). converge strongly in W. to a particular solution of the relaxed problem. Indeed, the so-selected solution is characterized as the unique solution of an auxiliary variational problem involving the integrand .↦ |.|.|.|.

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Nonlinear Averages and Convergence of Penalty Trajectories in Convex Programming, This particular limit point is characterized as the unique solution of a nested hierarchy of optimization problems. The construction leading to this hierarchy is based on asymptotic nonlinear averages, a notion which is described and studied in some detail.

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