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

Boshi Tian () and Xiaoxing Chang ()
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Boshi Tian: Hunan University
Xiaoxing Chang: Hunan University

Mathematical Methods of Operations Research, 2025, vol. 101, issue 1, No 5, 95-110

Abstract: 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.

Keywords: Nonlinear complementarity problem; Reweighted penalty method; Exponential rate of convergence; 90C26; 90C30; 90C33 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00186-024-00886-9

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