Optimization Reformulations Of The Generalized Complementarity Problem And Their Applications

The generalized complementarity problem over the polyhedral cone (GNCP) is considered in this thesis, which contains the following contents:In chapter 1, we reformulate GNCP as two constrained optimization problems and give the conditions under which their KKT points are solutions of GNCP, then we give an unconstrained optimization reformulation of GNCP and give the conditions under which its stationary point is a solution of GNCP.In chapter 2, based on the unconstrained optimization reformulation of GNCP given in chapter 1, we design a Newton-type method for solving it without using the second-order derivatives of F and G. Under suitable conditions, we show that this method converges quadratically.