Yang Cao
Department of Transportation and Civil Engineering, Nantong University, PR China
The generalized absolute value equations (GAVE) arise in many areas of scientific computing and engineering applications, such as linear programming, bimatrix games, quadratic programming and so on. The well-known linear complementarity problem (LCP) can be transformed into the GAVE, and vice versa. Due to the existence of the absolute term, the GAVE is often regarded as a system of non-differentiable and nonlinear equations.
In this talk, we will first show some interesting applications, including a traffic single bottleneck model, and then present a class of modified Newton-type iteration methods which are constructed by separating the differential and the non-differentiable parts of the generalized absolute value equations. The new modified Newton-type iteration method involves the well-known Picard iteration method as the special case. Convergence properties of the new iteration schemes are analyzed in detail. In particular, some specific sufficient conditions are presented for two special coefficient matrices. Finally, some numerical examples will be given to illustrate the effectiveness of the proposed modified Newton-type iteration methods.