Components identification based method for box constrained variational inequality problems with almost linear functions
For finding the solution \(x^{\ast}\) of a mixed complementarity problem in form of a variational inequality with box constraints \((y - x^{\ast})^T F(x^{\ast}) \geq 0 \;\; \forall y \in [l, u] \) and with almost linear functions \(F(x) = Mx + \varphi(x)\) an iterative algorithm is developed. The algorithm computes an approximate solution by solving at most \(n\) reduced systems of equations. Only the one of the smallest dimension has to be solved with high accuracy, the others are solved merely to identify some components of the solution. The performance of the algorithm is demonstrated numerically for a finite element discretized obstacle problem. The numerical results show that the algorithm is more efficient than the semi-smooth Newton method of \textit{C. Kanzow} and \textit{M. Fukushima} [Oper. Res. Lett. 23, No. 1--2, 45--51 (1998; Zbl 0941.90070)].
scientific article; zbMATH DE number 5549594
scientific article