首页 | 本学科首页 官方微博 | 高级检索
 全部专业 化学 晶体学 力学 数学 物理学 学报及综合类   按 中文标题 英文标题 中文关键词 英文关键词 中文摘要 英文摘要 作者中文名 作者英文名 单位中文名 单位英文名 基金中文名 基金英文名 杂志中文名 杂志英文名 栏目英文名 栏目英文名 DOI 责任编辑 分类号 杂志ISSN号 检索

 求解不可微箱约束变分不等式的下降算法 引用本文： 陈国庆,刘水霞.求解不可微箱约束变分不等式的下降算法[J].高等学校计算数学学报,2002,24(4):335-348. 作者姓名： 陈国庆  刘水霞 作者单位： 内蒙古大学理工学院数学系,呼和浩特,010021 基金项目： 国家自然科学基金(19701016)，内蒙古自然科学基金资助. 摘    要： 1 引 论 设X(?)Rn是非空闭集,F:Rn→Rn连续映射,变分不等式问题VI(X,F)是指:求x∈X,使 F(x)T(y-x)≥0,　 (?)y∈X,(1)记指标集N=(1,2,…,n},当 X=a,b]≡{x∈Rn|a≤xi≤bi,i∈N},(2)其中a={a1,a2,…,an}T,b={b1,b2,…,bn}T∈Rn时,VI(X,F)化为箱约束变分不等式VI(a,b,F).若ai=0,bi=+∞,i∈N,即X=R+n≡{x∈Rn|x≥0}时,VI(a,b,F)化为非线性 关 键 词： 不可微箱约束  变分不等式  下降算法 SOLUTION OF BOX CONSTRAINED VARIATIONAL INEQUALITY WITH LOCALLY LIPSCHITZIAN FUNCTIONS Chen Guoqing Liu Shuixia.SOLUTION OF BOX CONSTRAINED VARIATIONAL INEQUALITY WITH LOCALLY LIPSCHITZIAN FUNCTIONS[J].Numerical Mathematics A Journal of Chinese Universities,2002,24(4):335-348. Authors: Chen Guoqing Liu Shuixia Abstract: A new unconstrained merit function (x) for the box constrained variational inequality VI(a,b,F) with locally Lipschitzian function F (need not be differentiable) is proposed and its various desirable properties are investigated. Using this merit function the box constrained variational inequality is reformulated as the unconstrained minimization problem min{(x) |xRn}. When every V F(x) is P0-matrix, it is proved that 0(x) is necessary and sufficient for x to be a solution to VI(a,b,F). Based on these special properties, for monotone functions F a simple derivative-free algorithm with global convergence for solving min{0(x) |xRn} is proposed. Moreover, a generalized Newton method is also presented. Under the suitable regularity condition it is proved that the method is locally well defined and superlinearly convergent for semismooth functions F and quadratically convergent for strongly semismooth functions F respectively. Keywords: box constrained variational inequality with locally Lipschitzian func-tions  merit functions  derivative-free algorithm  generalized Newton method 本文献已被 CNKI 维普 万方数据 等数据库收录！