扰动Newton法求解函数互补问题

把R0 -矩阵的概念推广到了非线性互补问题 (NLCP) :y - f(x) =0 ,x y =(x1y1,… ,xnyn) T=0 ,x ,y∈Rn+ 的情形 ,应用扰动Newton法求解当 f :Rn→Rn是连续可微的P0 -函数时的互补问题。在无严格互补解的条件下证明了若 f(x)是一个连续可微的P0 -函数 ,满足李卜西兹条件 ,且存在一个常数c>0和 0 <ε≤ 1对所有x∈Rn+ 有 fi0 (x) - fi0 (0 )≥c‖x‖ε,其中 ,xki0 =maxi∈I{xki}成立 ,则产生的序列 { ωk}大范围收敛到NLCP的解。并证明了若 ( f(x ) ) γ γ是一个P矩阵 ,那么序列 { ωk}Q - 2阶收敛到NLCP的解ω 。

A Perturbed Newton Method for Solving P0-Function Complementarity Problems

The concept of R 0-matrix was generalized to non-linear complementraity problems(NLCP). A perturbed Newton method was used to solve P 0-function f:R n→R n complementraity problems, y-f(x)=0,xy=(x 1y 1,...,x ny n) T=0, x,y∈R n + and under the condition without strict complementarity slackness it was proved that, if f:R n→R n is a continuously differentiable P 0-function, satisfying Lipschitz condition,and there exists constants c>0 and 0<ε≤1,for all x∈R n +, f i 0(x)-f i 0(0)≥c‖x‖ ε,holds,where x k i 0= max i∈I {x k i},then the sequence { k} globally converges to ω *.And if (f(x *)) is a P-matrix,then the sequence { k} Q-quadratically converges to ω *.