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Optimierung konvexer Funktionen mit Stabilitätsbetrachtungen

Peter Kosmol — 1976

INHALTSVERZEICHNISEinleitung....................................................................................................................... 5§ 1. Existenz der Minimallösungen................................................................... 7§ 2. Modulare Optimierung......................................................................................... 9§ 3. Der Satz von Banach-Steinhaus für konvexe Funktionen.............................. 17§ 4. Stabilität bei nichtlinearer Optimierung...............................................................

Pointwise minimization of supplemented variational problems

Peter Kosmol;  Dieter Müller-Wichards — 2004

Colloquium Mathematicae

We describe an approach to variational problems, where the solutions appear as pointwise (finite-dimensional) minima for fixed t of the supplemented Lagrangian. The minimization is performed simultaneously with respect to the state variable x and ẋ, as opposed to Pontryagin's maximum principle, where optimization is done only with respect to the ẋ-variable. We use the idea of the equivalent problems of Carathéodory employing suitable (and simple) supplements to the original minimization problem....

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