On The Error Bound Estimation And A New Algorithm Of The Generalized Complementarity Problem Over A Polyhedral Cone

In this thesis, the error bound estimation of the generalized complementarity problem over a polyhedral cone is considered and a new type of solution method for the problem is proposed. The thesis consists of three chapters.In Chapter 1, we mainly give a short retrospect to the existing results to the concerned problem and the main contributions of this thesis.In Chapter 2, we mainly establish the error estimation of the GNCP. To this end, we first reformulate the concerned problem as a mixed complementarity problem(MCP), and then we estimate the error bound estimation of the GNCP based on the related results on the latter problem. To guarantee that the error bound estimation holds, we discussed the relations between the error bound, the semistability and 2-regularity of the solutions. Second, we give a sufficient condition of the weak regularity . In the end, we show that the semi-stability, 2-regularity and weak regularity are equivalent under the condition of strict complementarity.In Chapter 3, based on the conditions of GNCP given in the last chapter, we design a Newton-type method for solving it based on the acting-set identification technique. The weak regularity of the solutions is shown to be an necessary and sufficient conditions for the convergence of the proposed method. In particular, we show that the weak regularity is weaker than the existing conditions given in the literature. By combining this method with descent methodand NCP function, we establish a globally convergent method for the GNCP. Under weaker conditions, we show that this method converges quadratically.