Abstract
In this paper, we consider a kernel-based full-Newton step feasible interior-point method (IPM) for P∗(κ)-Weighted Linear Complementarity Problem (WLCP). The specific eligible kernel function is used to define an equivalent form of the central path, the proximity measure, and to obtain search directions. Full-Newton steps are adopted to avoid the line search at each iteration. It is shown that with appropriate choices of the parameters, and a certain condition on the starting point, the iterations always lie in the defined neighborhood of the central path. Assuming strict feasibility of P∗(κ)-WLCP, it is shown that the IPM converges to the ε-approximate solution of P∗(κ)-WLCP in a polynomial number of iterations. Few numerical results are provided to indicate the computational performance of the algorithm.
Original language | English |
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Pages (from-to) | 108-132 |
Number of pages | 25 |
Journal | Journal of Optimization Theory and Applications |
Volume | 202 |
Issue number | 1 |
DOIs | |
State | Published - Jul 2024 |
Scopus Subject Areas
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics
Keywords
- Full-Newton step
- Interior-point algorithm
- P(κ)-weighted linear complementarity problem
- Polynomial complexity