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Homotopy Continuation Method for Linear Complementarity Problems

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Northeastern Mathematical Journal 2004年第3期20卷 309-316页

作者：刘国新于波 School of Mathematics Jilin University Changchun 130012 Department of Applied Mathematics Dalian University of Technology Dalian 116024t is well known that a linear complementarity problem (LCP) can be formulated as a system of nonsmooth equations F(x) = 0 where F is a map from Rninto itself. Using the aggregate function we construct a smooth Newton homotopy H(xt) = 0. Under certain assumptions we prove the existence of a smooth path defined by the Newton homotopy which leads to a solution of the original problem and study limiting properties of the homotopy path.

It is well known that a linear complementarity problem (LCP) can be formulated as a system of nonsmooth equations F(x) = 0, where F is a map from Rninto itself. Using the aggregate function, we construct a smooth Newton homotopy H(x,t) = 0. Under certain assumptions, we prove the existence of a smooth path defined by the Newton homotopy which leads to a solution of the original problem, and study limiting properties of the homotopy path.

关键词： linear complementarity aggregate function homotopy method

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The aggregate Homotopy Method for Constrained Sequential Max-min Problems

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Northeastern Mathematical Journal 2003年第4期19卷 287-290页

作者：于波刘国新冯果忱李勇 Department of Applied Mathematics Dalian University of Technology Dalian 116024 institute of Mathematics Jilin University Changchun 130012 Communicated

Consider the constrained sequential max-min problem(CSMMP):

关键词： nonsmooth programming aggregate function interior point method homotopy method

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求解凸不等式问题的熵光滑化方法

高等学校计算数学学报 2004年第1期26卷 25-29页

作者：李兴斯张培爱大连理工大学力学系广州 510632 暨南大学数学系大连 116024

1 引言凸不等式问题f;（x）≤0,i=1,...,m.（1.1）这里函数f;（x）,i=1,……,m是凸函数,且假设不等式问题（1.1）存在有限的解。不等式问题是一类非常重要的基本问题,广泛地存在于工程、经济、交通、信息等领域。近几年来,光滑化方法... 详细信息

1 引言凸不等式问题f;（x）≤0,i=1,...,m.（1.1）这里函数f;（x）,i=1,……,m是凸函数,且假设不等式问题（1.1）存在有限的解。不等式问题是一类非常重要的基本问题,广泛地存在于工程、经济、交通、信息等领域。近几年来,光滑化方法是求解互补问题、变分不等式问题以及平衡约束数学规划问题的一个热点。1995年Chen-chunhui和Mangasarian基于神经网络函数

关键词： inequality problem aggregate function convergence.

Study on Multi-criteria Personalized Recommendation Algorithm

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Study on Multi-criteria Personalized Recommendation Algorith...