Original scientific paper
https://doi.org/10.17535/crorr.2018.0004
A full Nesterov-Todd step primal-dual path-following interior-point algorithm for semidefinite linear complementarity problems
Mohamed Achache
; Laboratory of Fundamental and Numerical Mathematics, Sétif1 University, Sétif, Algeria
Nersine Tabchouche
; Laboratory of Fundamental and Numerical Mathematics, Sétif1 University, Sétif, Algeria
Abstract
In this paper, a feasible primal-dual path-following interior-point algorithm for monotone semidefinite linear complementarity problems is proposed. At each iteration, the algorithm uses only full Nesterov-Todd feasible steps for tracing approximately the central-path and getting an approximated solution of this problem. Under a new appropriate choices of the threshold \(\tau\) which defines the size of the neighborhood of the central-path and of the update barrier parameter \(\theta\), we show that the algorithm is well-defined and enjoys the locally quadratically convergence. Moreover, we prove that the short-step algorithm deserves the best known iteration bound, namely, \(\O(\sqrt{n} log \frac{n}{\epsilon}))\). Finally, some numerical results are reported to show the practical performance of the algorithm.
Keywords
Semidefinite linear complementarity; Interior-point algorithm; Short-step method; Polynomial complexity
Hrčak ID:
203892
URI
Publication date:
24.7.2018.
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