George Isac, Monica G. Cojocaru, "The projection operator in a Hilbert space and its directional derivative. Consequences for the theory of projected dynamical systems", Journal of Function Spaces, vol. 2, Article ID 543714, 25 pages, 2004. https://doi.org/10.1155/2004/543714
The projection operator in a Hilbert space and its directional derivative. Consequences for the theory of projected dynamical systems
In the first part of this paper we present a representation theorem for the directional derivative of the metric projection operator in an arbitrary Hilbert space. As a consequence of the representation theorem, we present in the second part the development of the theory of projected dynamical systems in infinite dimensional Hilbert space. We show that this development is possible if we use the viable solutions of differential inclusions. We use also pseudomonotone operators.
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