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Matrix Optimization Over Low-Rank Spectral Sets: Stationary Points and Local and Global Minimizers

Author

Listed:
  • Xinrong Li

    (Beijing Jiaotong University)

  • Naihua Xiu

    (Beijing Jiaotong University)

  • Shenglong Zhou

    (University of Southampton)

Abstract

In this paper, we consider matrix optimization with the variable as a matrix that is constrained into a low-rank spectral set, where the low-rank spectral set is the intersection of a low-rank set and a spectral set. Three typical spectral sets are considered, yielding three low-rank spectral sets. For each low-rank spectral set, we first calculate the projection of a given point onto this set and the formula of its normal cone, based on which the induced stationary points of matrix optimization over low-rank spectral sets are then investigated. Finally, we reveal the relationship between each stationary point and each local/global minimizer.

Suggested Citation

  • Xinrong Li & Naihua Xiu & Shenglong Zhou, 2020. "Matrix Optimization Over Low-Rank Spectral Sets: Stationary Points and Local and Global Minimizers," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 895-930, March.
    • Handle: RePEc:spr:joptap:v:184:y:2020:i:3:d:10.1007_s10957-019-01606-8
    DOI: 10.1007/s10957-019-01606-8
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    Cited by:

    1. Yitian Qian & Shaohua Pan & Yulan Liu, 2023. "Calmness of partial perturbation to composite rank constraint systems and its applications," Journal of Global Optimization, Springer, vol. 85(4), pages 867-889, April.

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