Abstract
The primal-dual interior-point method is widely recognized as one of the most effective approaches for solving the linear complementarity problem. As an extension of the linear complementarity problem, the study of the weighted linear complementarity problem is more necessary. In this paper, a new full-Newton step primal-dual interior-point algorithm is proposed for the special weighted linear complementarity problem. At each iteration, the search directions of the method are determined via a positive-asymptotic kernel function. The iteration complexity of the algorithm is analyzed, and the result is the same as the currently best known complexity bound of the similar methods. Finally, the validity of the algorithm is verified by some numerical results.
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DZ and JZ contributed to the primary writing of the manuscript. DZ and MZ were responsible for the proofs of the theorems and lemmas presented in the paper. The creation of Tables 1, 2 and 3 was the responsibility of Dechun Zhu. All authors participated in the review and approval of the final manuscript.
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Zhang, M., Zhu, D. & Zhong, J. A full-Newton step interior-point algorithm for the special weighted linear complementarity problem based on positive-asymptotic kernel function. Optim Eng (2023). https://doi.org/10.1007/s11081-023-09873-1
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DOI: https://doi.org/10.1007/s11081-023-09873-1
Keywords
- Full-Newton step
- Interior-point methods
- Weighted linear complementarity
- Positive-asymptotic kernel function