Strong Convergence of a Two-Step Modified Newton Method for Weighted Complementarity Problems

This paper focuses on the weighted complementarity problem (WCP), which is widely used in fields of economics, sciences and engineering. Not least because its local superlinear convergence rate, smoothing Newton methods have widespread application solving various optimization problems. A two-step method with strong proposed. With a complementary function, WCP reformulated as set equations solved by proposed method. In each iteration, new computes equation twice, but using same Jacobian, can avoid consuming lot time calculation. To ensure global convergence, derivative-free line search rule inserted. At time, we develop different term solution equation, guarantees convergence. Under appropriate conditions, algorithm has at quadratic or even cubic Numerical experiments indicate stability effectiveness Moreover, compared to general method, significantly improve computational efficiency without increasing cost.