Banach 空间中多值非单调算子的相补问题

应用H-空间中的Park极大元定理,在Banach空间中证明了多值非单调算子的相补问题的解的存在性定理．     

多值单调算子的隐补问题

在Banach空间中引入了多值算子的隐补问题和相补问题的新概念，并证明了多值单调算子隐补问题和相补问题解的存在性定理。     

混合单调算子方程解存在与唯一性定理及应用

本文在不假定算子具有紧性，连续性或对称压缩的条件下，研究了混合单调算子方程解的存在与唯一性。     

关于正a齐次算子方程的一个定理及其应用

本文在较宽松的条件下，研究了正ａ齐次算子方程（ａ〉１）解的存在唯一性并给出了应用。     

一类K-单调系统产生的K-单调算子

本文研究了K-单调系统的解的渐近性质.应用K-单调算子的性质,得到了保证K-单调系统的正周期解的存在性、唯一性、全局渐近稳定性的充分条件.     

一类K-单调系统产生的K-单调算子

本文研究了Ｋ－单调系统的解的渐近性质．应用Ｋ－单调算子的性质,得到了保证Ｋ－单调系统的正周期解的存在性、唯一性、全局渐近稳定性的充分条件．     

一类非混合单调算子方程的耦合解定理及其非单调迭代算法

研究无穷维序Banach空间中一类非混合单调算子，它可以表示成T=T1 T2，其中T1是混合单调算子，T2是反向混合单调算子(T2≠0)，得到了其耦合解的存在性定理．当尸是正规极小锥时，通过构造一系列确界生成序列，建立了耦合解的非单调迭代算法．置后，推广了最大一最小解的概念，定义了极大一极小解并研究了其存在的条件．     

p-Laplacian奇异半正单调问题的非负解

运用分析的方法，建立了具有p-Laplacian算子的二阶奇异半正单调边值问题的非负解的存在性条件．     

一类T单调算子障碍问题的块单调迭代法

本文对一类T单调算子的障碍问题提出了几个块迭代法．所得的迭代序列为上解序列和下解序列,它们均单调收敛于问题的准确解,本文建立了这些算法的比较定理．     

Park不动点定理与多值单调算子的隐补问题

应用Park不动点定理,在Banach空间中证明了多值单调算子的隐补问题解的存在性定理.     

局部凸空间中多值单调算子的隐补问题

应用Fan Ky定理讨论了局部凸空间中多值单调算子的隐补问题.     

带紧扰动的单调算子的特征值问题

使用新的逼近技巧研究了紧扰动下单调算子的特征值问题，所得结果改进并推广了Guan和Kartsatos最近的某些结果．     

Regular Maximal Monotone Operators

The purpose of this paper is to introduce a class of maximal monotone operators on Banach spaces that contains all maximal monotone operators on reflexive spaces, all subdifferential operators of proper, lsc, convex functions, and, more generally, all maximal monotone operators that verify the simplest possible sum theorem. Dually strongly maximal monotone operators are also contained in this class. We shall prove that if T is an operator in this class, then (the norm closure of its domain) is convex, the interior of co(dom(T)) (the convex hull of the domain of T) is exactly the set of all points of at which T is locally bounded, and T is maximal monotone locally, as well as other results.     

Extended LQP Method for Monotone Nonlinear Complementarity Problems

To solve nonlinear complementarity problems (NCP), the logarithmic-quadratic proximal (LQP) method solves a system of nonlinear equations at each iteration. In this paper, the iterates generated by the original LQP method are extended by explicit formulas and thus an extended LQP method is presented. It is proved theoretically that the lower bound of the progress obtained by the extended LQP method is greater than that by the original LQP method. Preliminary numerical results are provided to verify the theoretical assertions and the effectiveness of both the original and the extended LQP method.     

P*(k)线性互补问题的Mehrotra型预估-校正算法复杂性分析

本文提出一种求解单调非线性互补问题的Mehrotra型预估-校正算法.新算法采用不同的自适应更新策略.在尺度化的Lipschitz条件下,证明了新算法的迭代复杂性为O(n2 log (x0)T s0/ε)),其中(x0,s0)为初始点,ε为精度.     

A Complexity Analysis of a Smoothing Method Using CHKS-functions for Monotone Linear Complementarity Problems

We consider the standard linear complementarity problem (LCP): Find (x, y) R ²ⁿ such that y = M x + q, (x, y) 0 and x _i y _i = 0 (i = 1, 2, ... , n), where M is an n × n matrix and q is an n-dimensional vector. Recently several smoothing methods have been developed for solving monotone and/or P ₀ LCPs. The aim of this paper is to derive a complexity bound of smoothing methods using Chen-Harker-Kanzow-Smale functions in the case where the monotone LCP has a feasible interior point. After a smoothing method is provided, some properties of the CHKS-function are described. As a consequence, we show that the algorithm terminates in Newton iterations where is a number which depends on the problem and the initial point. We also discuss some relationships between the interior point methods and the smoothing methods.     

Derivative-Free Methods for Monotone Variational Inequality and Complementarity Problems

Monotone variational inequality problems with box constraints and complementarity problems are reformulated as simple-bound optimization problems. Some derivative-free methods for these problems are proposed. It is shown that, for these new methods, the updated point sequence remains feasible with respect to its simple constraints if the initial point is feasible. Under certain conditions, these methods are globally convergent.