Derivative-free descent method for nonlinear complementarity problem via square Penalized Fischer-Burmeister function

The nonlinear complementarity problem (NCP) has been served as a general framework for linear, quadratic, and nonlinear programming, linear complementarity problem, and some equilibrium problems. Applications of the NCP can be found in many important fields such as economics, mathematical programming, operations research, engineering and mechanics. In this article, we consider smooth NCP on the basis of the square penalized Fischer-Burmeister function. We show under certain assumptions, any stationary point of the unconstrained minimization problem is already a solution of smooth NCP. Furthermore, a derivative-free descent algorithm is suggested and conditions for its convergence are given. Finally, some preliminary numerical results are presented.