Analysis of nonsmooth vector-valued functions associated with infinite-dimensional second-order cones |
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Authors: | Ching-Yu Yang Yu-Lin Chang Jein-Shan Chen |
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Institution: | Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan |
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Abstract: | Given a Hilbert space H, the infinite-dimensional Lorentz/second-order cone K is introduced. For any x∈H, a spectral decomposition is introduced, and for any function f:R→R, we define a corresponding vector-valued function fH(x) on Hilbert space H by applying f to the spectral values of the spectral decomposition of x∈H with respect to K. We show that this vector-valued function inherits from f the properties of continuity, Lipschitz continuity, differentiability, smoothness, as well as s-semismoothness. These results can be helpful for designing and analyzing solution methods for solving infinite-dimensional second-order cone programs and complementarity problems. |
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Keywords: | Hilbert space Infinite-dimensional second-order cone Strong semismoothness |
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