Clarke Generalized Jacobian of the Projection onto Symmetric Cones

Abstract

In this paper, we give an exact expression for Clarke generalized Jacobian of the projection onto symmetric cones, which generalizes and unifies the existing related results on secondorder cones and the cones of symmetric positive semi-definite matrices over the reals. Our characterization of the Clarke generalized Jacobian exposes a connection to rank-one matrices.

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