A derivative-free line search technique for Broyden-like method with applications to NCP, wLCP and SI

We propose a new derivative-free line search technique which contains the classical Li-Fukushima derivative-free line search [Optim. Methods Softw. 13 (3), 181–201, 2000] as a special case. The new line search can enable us to choose a larger step size at each iteration and reduce the number of function evaluations at each step. Based on the new line search, we prove that Broyden-like method for solving the nonlinear equation is globally and locally superlinearly convergent under appropriate assumptions. Moreover, we present some nonlinear equations arising from nonlinear complementarity problems (NCP), weighted linear complementarity problems (wLCP) and system of inequalities (SI). Numerical results show that Broyden-like method based on the new line search has better numerical performance than that based on Li-Fukushima line search.