A Modified Smoothing Newton Method for Solving Weighted Complementarity Problems with a Nonmonotone Line Search

we concentrate on the general form of the weighted complementarity problem, which serves as a generalization of the nonlinear complementarity problem and finds extensive applications in various fields, including economics, sciences, engineering, atmospheric chemistry, and multibody dynamics. We introduce a novel Fischer-Burmeister-based one-parameter smoothing complementarity function. The WCP is then reformulated as a smoothing system of equations, and a new smoothing Newton method is devised to solve the problem efficiently on the new one-parameter smoothing complementarity function. To ensure global convergence, we introduce a new line search rule. The new method exhibits both global and local quadratic convergence properties under appropriate conditions, as demonstrated through several numerical experiments that confirm its effectiveness and stability.