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An Accelerated Double-Proximal Gradient Algorithm for DC Programming

Author

Listed:
  • Gaoxi Li

    (School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, P. R. China)

  • Ying Yi

    (School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, P. R. China)

  • Yingquan Huang

    (Chongqing Key Laboratory of Social Economy and Applied Statistics, Chongqing 400067, P. R. China)

Abstract

The double-proximal gradient algorithm (DPGA) is a new variant of the classical difference-of-convex algorithm (DCA) for solving difference-of-convex (DC) optimization problems. In this paper, we propose an accelerated version of the double-proximal gradient algorithm for DC programming, in which the objective function consists of three convex modules (only one module is smooth). We establish convergence of the sequence generated by our algorithm if the objective function satisfies the Kurdyka–Šojasiewicz (KŠ) property and show that its convergence rate is not weaker than DPGA. Compared with DPGA, the numerical experiments on an image processing model show that the number of iterations of ADPGA is reduced by 43.57% and the running time is reduced by 43.47% on average.

Suggested Citation

  • Gaoxi Li & Ying Yi & Yingquan Huang, 2024. "An Accelerated Double-Proximal Gradient Algorithm for DC Programming," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 41(03), pages 1-21, June.
    • Handle: RePEc:wsi:apjorx:v:41:y:2024:i:03:n:s0217595923500288
    DOI: 10.1142/S0217595923500288
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