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Clarke Generalized Jacobian of the Projection onto Symmetric Cones

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Abstract

In this paper, we give an exact expression for Clarke generalized Jacobian of the projection onto symmetric cones, which generalizes and unifies the existing related results on second-order cones and the cones of symmetric positive semi-definite matrices over the reals. Our characterization of the Clarke generalized Jacobian exposes a connection to rank-one matrices.

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Authors and Affiliations

  1. Department of Applied Mathematics, Beijing Jiaotong University, Beijing, 100044, People’s Republic of China

    Lingchen Kong & Naihua Xiu

  2. Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    Lingchen Kong & Levent Tunçel

Authors
  1. Lingchen Kong
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  2. Levent Tunçel
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  3. Naihua Xiu
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Correspondence to Lingchen Kong.

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Kong, L., Tunçel, L. & Xiu, N. Clarke Generalized Jacobian of the Projection onto Symmetric Cones. Set-Valued Anal 17, 135–151 (2009). https://doi.org/10.1007/s11228-009-0113-4

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  • DOI: https://doi.org/10.1007/s11228-009-0113-4

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