Abstract
This paper analyses the properties of the projection mapping over a set defined by a constraint function whose image is possibly a nonpolyhedral convex set. Under some nondegeneracy assumptions, we prove the (strong) semismoothness of the projection mapping. In particular, we derive the strong semismoothness of the projection mapping when the nonpolyhedral convex set under consideration is taken to be the second-order cone or the semidefinite cone. We also derive the semismoothness of the solution to the Moreau–Yosida regularization of the maximum eigenvalue function.
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Goh, M., Meng, F. On the Semismoothness of Projection Mappings and Maximum Eigenvalue Functions. J Glob Optim 35, 653–673 (2006). https://doi.org/10.1007/s10898-005-5880-3
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DOI: https://doi.org/10.1007/s10898-005-5880-3