Friday, 11:30 - 11:55 h, Room: H 2051

 

Vladimir Goncharov
Well-posedness of minimal time problem with constant convex dynamics via differential properties of the value function

Coauthors: Giovanni Colombo, Boris Mordukhovich

 

Abstract:
We consider a general minimal time problem with a constant convex dynamics in a (reflexive) Banach space, which can be seen as a mathematical programming problem. First, we obtain a general formula for the minimal time projection onto a closed set in terms of the duality mapping associated with the dynamics. Based on this formula we deduce then necessary and sufficient conditions of existence and uniqueness of a minimizer in terms of either dynamics rotundity (equivalently, smoothness of the dual set) or differential properties of the target. In both cases the (Fr├ęchet) differentiability of the value function is extremely relevant. Some counter-examples are presented.

 

Talk 3 of the invited session Fri.1.H 2051
"Generalized differentiation and applications" [...]
Cluster 24
"Variational analysis" [...]

 

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