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A reweighted $$\ell _1$$ ℓ 1 -penalty method for nonlinear complementarity problems

Author

Listed:
  • Boshi Tian

    (Hunan University)

  • Xiaoxing Chang

    (Hunan University)

Abstract

In this paper, we introduce a reweighted $$\ell _1$$ ℓ 1 -penalty method for solving the nonlinear complementarity problem. The novel method not only keeps the semismooth property of the classical $$\ell _1$$ ℓ 1 -penalty method, but also it has the advantage of the exponential rate of convergence. Specifically, under mild conditions, we prove that there exists some iterative sequence converging to a solution of the original problem with an exponential rate of convergence. Moreover, the semismooth Newton method can be used to efficiently solve the reweighted $$\ell _1$$ ℓ 1 -penalized equations. Finally, we carry out numerical experiments on test problems from MCPLIB and infinite-dimensional optimization problems. Numerical results show that the proposed method can solve these problems with fewer function evaluations than that of some existing numerical methods.

Suggested Citation

  • Boshi Tian & Xiaoxing Chang, 2025. "A reweighted $$\ell _1$$ ℓ 1 -penalty method for nonlinear complementarity problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 101(1), pages 95-110, February.
    • Handle: RePEc:spr:mathme:v:101:y:2025:i:1:d:10.1007_s00186-024-00886-9
    DOI: 10.1007/s00186-024-00886-9
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