Solving non‐linear complementarity problem by a derivative‐free descent method

The non‐linear complementarity problem (NCP) has many important applications in operations research, economic equilibrium, models, mathematical programming, engineering and mechanics. In this paper, we consider smooth NCP on the basis of the square Kanzow Kleinmichel function. We show under certain assumptions, any stationary point of the unconstrained minimisation problem is already a solution of smooth NCP. Also, we suggest a derivative‐free descent algorithm and give conditions for its convergence. Furthermore, we present some preliminary numerical results.