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Analysis of nonsmooth vector-valued functions associated with second-order cones

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Abstract.

Let be the Lorentz/second-order cone in . For any function f from to , one can define a corresponding function fsoc(x) on by applying f to the spectral values of the spectral decomposition of x∈ with respect to . We show that this vector-valued function inherits from f the properties of continuity, (local) Lipschitz continuity, directional differentiability, Fréchet differentiability, continuous differentiability, as well as (ρ-order) semismoothness. These results are useful for designing and analyzing smoothing methods and nonsmooth methods for solving second-order cone programs and complementarity problems.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, Seattle, WA 98195, USA

    Jein-Shan Chen, Xin Chen & Paul Tseng

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  1. Jein-Shan Chen
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  2. Xin Chen
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  3. Paul Tseng
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Correspondence to Paul Tseng.

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Mathematics Subject Classification (1991): 26A27, 26B05, 26B35, 49J52, 90C33, 65K05

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Chen, JS., Chen, X. & Tseng, P. Analysis of nonsmooth vector-valued functions associated with second-order cones. Math. Program., Ser. A 101, 95–117 (2004). https://doi.org/10.1007/s10107-004-0538-3

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