Complexity analysis of a weighted-full-Newton step interior-point algorithm for $P_{*}\left(\kappa \right)$-LCP

Achache, Mohamed

RAIRO - Operations Research - Recherche Opérationnelle, Tome 50 (2016) no. 1, pp. 131-143.

In this paper, a weighted-path-following interior point algorithm for $P_{*}\left(\kappa \right)$-linear complementarity problems ($P_{*}\left(\kappa \right)$-LCP) is presented. The algorithm uses at each weighted interior point iteration only feasible full-Newton steps and the strategy of the central-path for getting a solution for $P_{*}\left(\kappa \right)$-LCP. We prove that the proposed algorithm has quadratically convergent with polynomial time. The complexity bound, namely, $O((1+\kappa )\sqrt{n}log\frac{n}{ϵ})$ of the algorithm is obtained. Few numerical tests are reported to show the efficiency of the algorithm.

Classification : 90C33, 90C51, 11Y16
Mots clés : Linear complementarity problems, P_∗(κ)-matrix, weighted-path-following, interior-point methods, polynomial complexity

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