On the semismoothness of projection mappings and maximum eigenvalue functions
Goh, M. Meng, F.
Meng, F.
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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. © Springer 2006.
Keywords
Maximum eigenvalue functions, Moreau-Yosida regularization, Projection mappings, Semidefinite cones, Semismooth functions
Source Title
Journal of Global Optimization
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Date
2006
DOI
10.1007/s10898-005-5880-3
Type
Article