ABSTRACT
We provide a new proof of the Pontryagin Maximum Principle for problems with state constraints of the form https://www.w3.org/1998/Math/MathML"> g(t; x(t))_ 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315177991/9662f332-a51c-4039-a3db-8bac5c7e3e5d/content/eq550.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> using a technique of exact penalization. In particular, we show how to use two theorems of nonsmooth analysis, namely the multidirectional mean value inequality of Clarke and Ledyaev and a subgradient formula for maximum-type functions due to Ledyaev and Trieman, to derive the Pontryagin Maximum Principle for problems with state constraints and to derive viability-type results for state constrained problems.
