On the Projections of Multivalued Maps

U. Raitums

Journal of Optimization Theory and Applications, 1997, vol. 92, issue 3, No 9, 633-660

Abstract: Abstract This paper considers analogues of the Helmholtz projections of the set Π′ of selections of a piecewise smooth multivalued map $$\prod :R^n \to 2^{R^{m \times n} } $$ , n≥2. It is shown that, for m≤n−1 (m=1), the closure of the projection of Π′ on the subspace of gradient fields (solenoidal vector fields) is a convex set. For the general case, there are given point-wise conditions on the values of the map Π which ensure that the closure of the projection of Π′ contains the zero element. Possible applications to optimal control problems are discussed.

Keywords: Multivalued maps; Helmholtz projection; rank r convex hull; extensions of optimal control problems (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1023/A:1022611608062

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