Kernel-Based Full-Newton Step Feasible Interior-Point Algorithm for P(κ) -Weighted Linear Complementarity Problem

Xiaoni Chi, Guoqiang Wang, Goran Lesaja

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)108-132
Number of pages25
JournalJournal of Optimization Theory and Applications
Volume202
Issue number1
DOIs
StatePublished - 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

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