Every compact convex subset of matrices is the Clarke Jacobian of some Lipschitzian mapping

Abstract: Given a non-empty compact convex subset $P$ of $m \times n$ matrices, we show constructively that there exists a Lipschitzian mapping $g\colon {\bf R}^n \to {\bf R}^m$ such that its Clarke Jacobian $\partial g(0) = P$.

optimization and control

Audience: researchers in the topic

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