Exceptional Family of Elements for a Variational Inequality Problem and its Applications
Journal of Global Optimization
Global convergence enhancement of classical linesearch interior point methods for MCPs
Journal of Computational and Applied Mathematics
On a Class of Superlinearly Convergent Polynomial Time Interior Point Methods for Sufficient LCP
SIAM Journal on Optimization
On the equivalence of linear complementarity problems
Operations Research Letters
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A predictor--corrector algorithm is proposed for solving monotone linear complementarity problems (LCPs) from infeasible starting points. The algorithm terminates in $O(nL)$ steps either by finding a solution or by determining that the problem has no solution of norm less than a given number. The complexity of the algorithm depends on the quality of the starting point. If the problem is solvable and if a certain measure of feasibility at the starting point is small enough, then the algorithm finds a solution in $O(\sqrt{n}L)$ iterations. The algorithm requires two matrix factorizations and two backsolves per iteration. If the problem has a strictly complementary solution, then the algorithm is quadratically convergent, and, therefore, its asymptotic efficiency index is $\sqrt{2}$.