Croatian Operational Research Review, Vol. 9 No. 1, 2018.

Izvorni znanstveni članak

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 ; Laboratoire de Mathématiques Fondamentales et Numériques, Université de Sétif1, Sétif, Algérie
Nersine Tabchouche ; Laboratoire de Mathématiques Fondamentales et Numériques, Université de Sétif1, Sétif, Algérie

Puni tekst:

str. 37-50

preuzimanja: 370

Sažetak

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.

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