Wednesday, 15:45 - 16:10 h, Room: H 2051

 

C. H. Jeffrey Pang
First order analysis of set-valued maps and differential inclusions

 

Abstract:
The framework of differential inclusions encompasses modern optimal control and the calculus of variations. Its analysis requires the use of set-valued maps. For a set-valued map, the tangential derivative and coderivatives separately characterize a first order sensitivity analysis property, or more precisely, a pseudo strict differentiability property. The characterization using tangential derivatives requires fewer assumptions. In finite dimensions, the coderivative characterization establishes a bijective relationship between the convexified limiting coderivatives and the pseudo strict derivatives. This result can be used to estimate the convexified limiting coderivatives of limits of set-valued maps. We apply these results to the study of differential inclusions by calculating the tangential derivatives and coderivatives of the reachable map, which leads to the subdifferential and subderivative dependence of the value function in terms of the initial conditions. These results in turn furthers our understanding of the Euler-Lagrange and transversality conditions in differential inclusions.

 

Talk 2 of the invited session Wed.3.H 2051
"Some stability aspects in optimization theory" [...]
Cluster 24
"Variational analysis" [...]

 

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