TY - JOUR
T1 - COMPLEXITY ANALYSIS OF A PREDICTOR-CORRECTOR INTERIOR-POINT ALGORITHM FOR P∗(κ)-WEIGHTED LINEAR COMPLEMENTARITY PROBLEMS
AU - Chi, Xiaoni
AU - Yang, Yuping
AU - Chen, Jein Shan
N1 - Publisher Copyright:
© (2025), (American Institute of Mathematical Sciences). All rights reserved.
PY - 2025/1
Y1 - 2025/1
N2 - This paper aims at a predictor-corrector interior-point algorithm for solving weighted linear complementarity problem with P∗(κ)-matrices, which is a variant of weighted complementarity problem and has wide applications in science, engineering, and economics. We first apply the algebraic equivalent transformation technique, and then use the identity function to determine the new search directions. Under suitable conditions, the feasibility and convergence of the algorithm are established. Moreover, we show that the proposed algorithm has polynomial-time complexity. As far as we know, this is the first predictor-corrector interior-point algorithm for P∗(κ)-weighted linear complementarity problem based on the above-mentioned search directions. Preliminary numerical results demonstrate that our algorithm performs well and efficiently on the test problems.
AB - This paper aims at a predictor-corrector interior-point algorithm for solving weighted linear complementarity problem with P∗(κ)-matrices, which is a variant of weighted complementarity problem and has wide applications in science, engineering, and economics. We first apply the algebraic equivalent transformation technique, and then use the identity function to determine the new search directions. Under suitable conditions, the feasibility and convergence of the algorithm are established. Moreover, we show that the proposed algorithm has polynomial-time complexity. As far as we know, this is the first predictor-corrector interior-point algorithm for P∗(κ)-weighted linear complementarity problem based on the above-mentioned search directions. Preliminary numerical results demonstrate that our algorithm performs well and efficiently on the test problems.
KW - P(k)-weighted linear complementarity problem
KW - Predictor-corrector interior-point algorithm
KW - polynomial-time complexity
KW - search direction
UR - https://www.scopus.com/pages/publications/85208456737
UR - https://www.scopus.com/pages/publications/85208456737#tab=citedBy
U2 - 10.3934/jimo.2024102
DO - 10.3934/jimo.2024102
M3 - Article
AN - SCOPUS:85208456737
SN - 1547-5816
VL - 21
SP - 731
EP - 750
JO - Journal of Industrial and Management Optimization
JF - Journal of Industrial and Management Optimization
IS - 1
ER -