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    Spectral operators of matrices: Semismoothness and characterizations of the generalized jacobian

    91260.pdf (301.1Kb)
    Access Status
    Open access
    Authors
    Ding, C.
    Sun, D.
    Sun, Jie
    Toh, K.C.
    Date
    2020
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Ding, C. and Sun, D. and Sun, J. and Toh, K.C. 2020. Spectral operators of matrices: Semismoothness and characterizations of the generalized jacobian. SIAM Journal on Optimization. 30 (1): pp. 630-659.
    Source Title
    SIAM Journal on Optimization
    DOI
    10.1137/18M1222235
    ISSN
    1052-6234
    Faculty
    Faculty of Science and Engineering
    School
    School of Elec Eng, Comp and Math Sci (EECMS)
    URI
    http://hdl.handle.net/20.500.11937/91436
    Collection
    • Curtin Research Publications
    Abstract

    Spectral operators of matrices proposed recently in [C. Ding, D. F. Sun, J. Sun, and K. C. Toh, Math. Program., 168 (2018), pp. 509{531] are a class of matrix-valued functions, which map matrices to matrices by applying a vector-to-vector function to all eigenvalues/singular values of the underlying matrices. Spectral operators play a crucial role in the study of various applications involving matrices such as matrix optimization problems that include semidefinite programming as one of most important example classes. In this paper, we will study more fundamental first- and second-order properties of spectral operators, including the Lipschitz continuity, ρ-order B(ouligand)-differentiability (0 < ρ≤ 1), ρ-order G-semismoothness (0 < ρ≤ 1), and characteriza- tion of generalized Jacobians.

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