线性对称锥规划的一步光滑牛顿法

基于光滑Fischer-Burmeister函数,给出求解线性对称锥规划的一步光滑牛顿法．该算法在每一步迭代只需求解一个线性方程组,并进行一次线性搜索．不必满足严格互补,算法具有全局收敛性．     

Smoothing inexact Newton method for solving P 0-NCP problems

Based on a smoothing symmetric disturbance FB-function, a smoothing inexact Newton method for solving the nonlinear complementarity problem with P0-function was proposed. It was proved that under mild conditions, the given algorithm performed global and superlinear convergence without strict complementarity. For the same linear complementarity problem （LCP）, the algorithm needs similar iteration times to the literature. However, its accuracy is improved by at least 4 orders with calculation time reduced by almost 50%, and the iterative number is insensitive to the size of the LCP. Moreover, fewer iterations and shorter time are required for solving the problem by using inexact Newton methods for different initial points.     

解P0非线性互补问题的非单调光滑牛顿法

基于CHKS光滑函数,将非线性互补问题转化为非线性光滑方程组,再构造光滑算子,将非线性光滑方程组转化为优化问题,且构造了一个新的牛顿算法,该算法引入了非单调线搜索,并在一定条件下证明了它的全局收敛性,及在非奇异条件而非严格互补条件条件下,证明了它的局部二次收敛性。最后给出数值实验结果。     

An inexact parameterized newton method for B-differentiable equations

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Smoothing Newton Algorithm for Nonlinear Complementarity Problem with a P.Function

By using a smoothing function,the P nonlinear complementarity problem(P NCP)can be reformulated as a parameterized smooth equation.A Newton method is proposed to solve this equation.The iteration sequence generated by the proposed algorithm is bounded and this algorithm is proved to be globally convergent under an assumption that the P NCP has a nonempty solution set.This assumption is weaker than the ones used in most existing smoothing algorithms.In particular,the solution obtained by the proposed algorithm is shown to be a maximally complementary solution of the P NCP without any additional assumption.     

The Embedding Method for Nonsmooth Equations

1IntroductionTherehavebeenmailystudiesonnonsllloothequatiollsl"'"]F(x)=0,FiD=R"-R",((l.l)butfewauthorsusedembedding1lletllodtosolve'theequations(1.l).In1990,S.M.RobinsonstudiedthenonsnlootllembeddingmethodforaclassofBdifferentiableequationsill[51.WhenFiss…     

二阶锥规划的光滑牛顿算法

基于光滑Fischer-Burmeister函数,给出一个求解二阶锥规划的光滑牛顿算法。算法对于初始点的选取没有任何限制,并且在每一步迭代时只需要求解一个线性方程组,只进行一次线搜索。同时在不满足严格互补的条件下,证明了算法是全局收敛的和局部二次收敛的。数值试验结果表明算法的有效性。