A nonmonotone derivative-free algorithm for nonlinear complementarity problems based on the new generalized penalized Fischer-Burmeister merit function
The authors propose a modified Fischer-Burmeister function to solve nonlinear complementarity problems. For this purpose, they combine two approaches from \textit{J.-S. Chen} et al. [J. Comput. Appl. Math. 232, No. 2, 455--471 (2009; Zbl 1175.65070)], i.e., an additional parameter \(\lambda\in(0,1)\) is introduced and the \(p\)th root with \(p\in (1,\infty)\) is considered instead of the square root. After analyzing the properties of the new merit function, the authors state a non-monotone derivative-free algorithm for the solution of a nonlinear complementarity problem (NCP). Subsequently, global convergence of the algorithm is shown for monotone functions defining the NCP. Using stronger conditions on the nonlinear function defining the NCP the authors also prove \(r\)-linear local convergence. Finally, numerical results are presented for several MCPLIB test problems.
scientific article; zbMATH DE number 5988294