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An indefinite proximal subgradient-based algorithm for nonsmooth composite optimization

Author

Listed:
  • Rui Liu

    (Beihang University)

  • Deren Han

    (Beihang University)

  • Yong Xia

    (Beihang University)

Abstract

We propose an indefinite proximal subgradient-based algorithm (IPSB) for solving nonsmooth composite optimization problems. IPSB is a generalization of the Nesterov’s dual algorithm, where an indefinite proximal term is added to the subproblems, which can make the subproblem easier and the algorithm efficient when an appropriate proximal operator is judiciously setting down. Under mild assumptions, we establish sublinear convergence of IPSB to a region of the optimal value. We also report some numerical results, demonstrating the efficiency of IPSB in comparing with the classical dual averaging-type algorithms.

Suggested Citation

  • Rui Liu & Deren Han & Yong Xia, 2023. "An indefinite proximal subgradient-based algorithm for nonsmooth composite optimization," Journal of Global Optimization, Springer, vol. 87(2), pages 533-550, November.
    • Handle: RePEc:spr:jglopt:v:87:y:2023:i:2:d:10.1007_s10898-022-01173-9
    DOI: 10.1007/s10898-022-01173-9
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