The Set-Valued Analysis (SVA) develops the classical concepts of continuity, derivative, measurability, integral, differential equation, etc., for functions whose "values" are sets. There are numerous motivations for this theory: optimization problems involving non-differentiable functions, modeling of control or uncertain (static or dynamic) systems, dynamics of geometrical shapes (mathematical morphology), etc. The language and the technique of the SVA became a part of the basic mathematical culture, and are particularly relevant to the mathematical economics. For example, the notion of integral of a set-valued function was introduced by the Nobel prize winner in economics Robert Aumann, and the famous general theory of existence of a price system equilibrating the economics was proved using SVA by another Nobel prize winner - Kenneth Arrow. Both theories will be a part of this lecture course, among others.
The lectures will be self-contained, in principle, but knowledge of functional analysis would be helpful. A comprehensive script written by the lecturer is available, including the preliminary material not included in the basic courses of differential and integral calculus and differential equations.
Wiedner Hauptstraße 8, gelber Bereich, 4. Stock, Seminarraum DBgelb04
Lecture notes for this course are available.
J.-P. Aubin and H. Frankowska. Set-valued analysis. Birkhäuser, Boston, Basel, Berlin, 1990.
K.Deimling. Multivalued Differential Equations. Walter de Gruyter, Berlin, New York, 1992.