Quadratic one-step smoothing Newton method for \(P_{0}\)-LCP without strict complementarity.
The linear complementarity problem with a matrix having all principal minors nonnegative is equivalent to a system of equations with Kanzow's smoothing function. This is solved by Newton's method involving only one linear system and only one Armijo-type line search. The algorithm has local quadratic convergence under nonsingularity condition. Boundedness of iterations is guaranteed by another condition. A comparison with methods from the literature is given and it is claimed that the algorithm has stronger convergence properties under weaker assumptions than many others.
scientific article; zbMATH DE number 1978089
scientific article