A derivative-free filter algorithm for nonlinear complementarity problem (Q861186)

The authors consider the nonlinear complementarity problem. The problem consists in finding a point \(x\in\mathbb{R}^n\) such that \(x\geq 0\), \(F(x)\geq 0\), \(x^TF(x)= 0\), where \(F: \mathbb{R}^n\to\mathbb{R}^n\) is a given continuously differentiable vector function. The paper presents a new derivative-free algorithm for solving this problem. The proposed algorithm makes use of the efficiency of the filter technique. Global convergence of the algorithm is proved under a monotonicity assumption of vector function \(F\). The concluding section contains three small illustrative examples (with \(n\leq 4\)) showing a better performance of the presented algorithm than the performance of an algorithm by \textit{K. Yamada}, \textit{N. Yamashita} and \textit{M. Fukushima} [Nonlinear Optimization and Related Topics, Kluwer Academic Publishers. Appl. Optim. 36, 463--487 (2000; Zbl 0996.90085)].