The global linear and local quadratic convergence of a non-interior continuation algorithm for the LCP
Zheng‐Hai Huang · IMA Journal of Numerical Analysis · 2005
In this paper, we propose a non-interior continuation algorithm for solving the P0-matrix linear complementarity problem (LCP), which is conceptually simpler than most existing non-interior continuation algorithms in the sense that the proposed algorithm only needs to solve at most one linear system of equations at each iteration. We show that the proposed algorithm is globally convergent under a common assumption. In particular, we show that the proposed algorithm is globally linearly and locally quadratically convergent under some assumptions which are weaker than those required in many existing non-interior continuation algorithms. It should be pointed out that the assumptions used in our analysis of both global linear and local quadratic convergence do not imply the uniqueness of the solution to the LCP concerned. To the best of our knowledge, such a convergence result has not been reported in the literature.