A nonmonotone derivative-free algorithm for nonlinear complementarity problems based on the new generalized penalized Fischer–Burmeister merit function

Abstract

In this paper, we propose a new generalized penalized Fischer---Burmeister merit function, and show that the function possesses a system of favorite properties. Moreover, for the merit function, we establish the boundedness of level set under a weaker condition. We also propose a derivative-free algorithm for nonlinear complementarity problems with a nonmonotone line search. More specifically, we show that the proposed algorithm is globally convergent and has a locally linear convergence rate. Numerical comparisons are also made with the merit function used by Chen (J Comput Appl Math 232:455---471, 2009), which confirm the superior behaviour of the new merit function.