绝对值方程和广义互补问题的算法研究.pdfVIP

 Æ℄Æ . , ÆÆ , . ,  , Lagrange , , . , ℄Æ, F-B , Broyden-like . , Æ.  . ; Æ; ; Broyden-like ; ; ii  Research About the Absolute Value Equation and the Generalized Nonlinear Complementarity Problem ABSTRACT This paper mainly studies the absolute value equation (AVE) and the gen- eralized nonlinear complementarity problem(GNCP) over the polyhedral cone. The structure of this paper is organized as follows. In chapter 1, some definitions and notations of the absolute value equation problem and the generalized nonlinear complementarity problem are introduced. Then, we summarize the main content of this paper. In chapter 2, we discuss a kind of absolute value equation problem Ax −|x| = n ×n n b, A ∈ R , b ∈ R . We first reformulate this problem as a smoothing convex Lagrange-dual programming and then suggest an efficient method for solving it. We show that the iteration sequence generated by the proposed algorithm converges globally in a finite iteration steps. In chapter 3, we consider the generalized nonlinear complementarity problem (GNCP) over a polyhedral cone. In this paper, based on a class of smoothing functions, a smoothing Broyden-like algorithm is proposed for solving it. Un- der suitable conditions, the iteration sequence generated by the proposed algo- rithm converges globally and superlinearly. Furthermore, the algorithm has local quadratic convergence under mild assumptions. Some numerical experiments show the efficiency of the proposed algorithm.