Properties Of A Family Of Generalized NCP-Functions And A Derivative-Free Algorithm For Complementarity Problems

The complementarity problem is an important branch in the mathematical pro-gramming field, which find wide applications in many fields such as engineering, eco-nomics and traffic equilibrium problem, therefore, it is significant to study the algo-rithms for solving complementarity problems. We introduce a family of new merit functions which are the generalization of several existing merit functions. We discuss a system of favorable properties of the proposed merit functions. By using the new merit functions, we propose a derivative-free algorithm for solving nonlinear complementarity problem. We show that the algorithm is globally convergent under suitable assump-tions. The preliminary numerical results are also reported, and the numerical results show that the proposed algorithm is effective.