【摘要】 <正> 非线性互补问题（记作NCP（F））定义为求x∈Rⁿ,满足X≥0,F（x）≥0且X^гF（x）=0。其中F:Rⁿ→Rⁿ。本文假设F（x）是一阶连续可微的。 引人映射H:Rⁿ→Rⁿ,其中H的第i个分量H_i（x）=min（x_i,F_i（x））及其L₁模函数 θ（x）=sum from i=1 to n |min(x_i,F_i（x）|设全集I={1,2,…,n},定义其子集: I_f（x）={i|F_i（x）<x_i}, I（x）={i|F_i（x）<x_i>0}, I（x）={i|F_i（x）=x_i},I_f（x）={i|F_i（x）<x_i<0} I_x={i|x_i<F_i（x）},I_f（x）={i|F_i（x）<x_i=0。其余子集I⁺（x）,I^-（x）,I⁰（x）,I⁺（x）,I_x^-（x）,I₀^x（x）定义同上。 又记J_f（x）=I\I_f（x）,定义Z:Rⁿ×Rⁿ→R,z（x,d）=sum from i=1 to n Z_i（x,d）,其中更多还原

【Abstract】 Nonlinear complementarity problems, denoted by NCP(F), play an important role in mathematical programming and some practical problems. In this paper, we present an iterative method for solving the nonlinear complementarity problems and prove its convergence. This L1-norm-type method can start with an arbitrary initial vector, and each iteration step consists essentially of the computation of F(x) and solving a linear programming only.更多还原