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An inexact successive quadratic approximation method for a class of difference-of-convex optimization problems

Author

Listed:
  • Tianxiang Liu

    (Tokyo Institute of Technology)

  • Akiko Takeda

    (The University of Tokyo
    Center for Advanced Intelligence Project)

Abstract

In this paper, we propose a new method for a class of difference-of-convex (DC) optimization problems, whose objective is the sum of a smooth function and a possibly non-prox-friendly DC function. The method sequentially solves subproblems constructed from a quadratic approximation of the smooth function and a linear majorization of the concave part of the DC function. We allow the subproblem to be solved inexactly, and propose a new inexact rule to characterize the inexactness of the approximate solution. For several classical algorithms applied to the subproblem, we derive practical termination criteria so as to obtain solutions satisfying the inexact rule. We also present some convergence results for our method, including the global subsequential convergence and a non-asymptotic complexity analysis. Finally, numerical experiments are conducted to illustrate the efficiency of our method.

Suggested Citation

  • Tianxiang Liu & Akiko Takeda, 2022. "An inexact successive quadratic approximation method for a class of difference-of-convex optimization problems," Computational Optimization and Applications, Springer, vol. 82(1), pages 141-173, May.
    • Handle: RePEc:spr:coopap:v:82:y:2022:i:1:d:10.1007_s10589-022-00357-z
    DOI: 10.1007/s10589-022-00357-z
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    References listed on IDEAS

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