一类非精确线性搜索共轭梯度新算法

本文通过对迭代参数的适当选取，给出了一类共轭梯度新算法。在算法的迭代过程中，迭代方向保持下降性，在一般的非精确线性搜索条件下，算法的全局收敛性得到了证明。     

离散信道容量的迭代算法

引入信息量偏差概念，给出平均交互信息量关于输入概率的增量公式，设计出离散信道容量线性乘法迭代和线性常系数迭代算法，它们都优于现有的指数迭代算法．并证明在所有单步迭代算法中它们几乎是最好的算法.     

Hilbert尺度下求解非线性不适定问题的多水平迭代法

本文吸取了多水平方法的思想，采用多水平方法提供了离散化参数和迭代初值的合理的选择方法，提出了Hilbert尺度下求解非线性不适定问题的多水平Landweber迭代算法，并给出了算法的收敛性分析，证明了算法在整体上提高了Hilbert尺度下的Landweber迭代法的迭代效率。     

一种提取小波脊线的迭代算法

在实际问题中，经常会需要识别信号的调制类型．小波脊线就包含了信号的重要特征．本文给出了提取小波脊线的一种迭代算法，以达到识别信号的目的，并将该算法与其他算法比较，表明迭代算法是一种行之有效的方法．     

基于Span压缩的相对值迭代算法

本文研究平均报酬马氏决策过程（MDP）的相对值迭代算法．给出了span半范数压缩因子的一个表达式，证明了该因子小于1时本文绘出的相对值迭代算法及小步长相对值迭代算法均收敛到其最优解．     

二次规划的内椭球算法

对于标准型的凸二次规划问题本文给出了一个新算法，算法的一每步迭代，利用内椭球的思想来近似求解一个线性质规划子问题而得到迭代方向，再适当选取步长而使之成为多项式算法，其迭代步数为Ｏ（ｎＬ＾２），每一步迭代所需计算量为Ｏ（ｎ＾３）。其中ｎ为变量个数，Ｌ为问题的输入长度。     

一个关于非对称距离的旅行商问题的迭代算法

本对非对称距离的旅行商问题，给出了一个迭代算法，并分析了此迭代算法的复杂度为M^nO(N^4)，其中，N是问题中旅行商所要经过的城镇数，M是两城镇间的最大距离。最后用实例对此算法进行了验算和说明。     

迭代反褶积算法

本文利用条件期望的性质，导出了迭代反褶积算法模型，并给出参数λ的极大似然估计，算例表明该算法是有效的。     

线性二级决策的最优边界面算法

本文给出线性二级决策的一种非迭代算法，并给出一个算例。     

非线性不等式约束最优化一个超线性与二次收敛的强次可行方法

本文讨论非线性不等式约束最优化问题，借助于序列线性方程组技术和强次可行方法思想，建立了问题的一个初始点任意的快速收敛新算法．在每次迭代中，算法只需解一个结构简单的线性方程组．算法的初始迭代点不仅可以是任意的，而且不使用罚函数和罚参数，在迭代过程中，迭代点列的可行性单调不减．在相对弱的假设下，算法具有较好的收敛性和收敛速度，即具有整体与强收敛性，超线性与二次收敛性．文中最后给出一些数值试验结果．     

A smoothing Newton algorithm for weighted linear complementarity problem

In this paper, we present a new smoothing Newton method for solving monotone weighted linear complementarity problem (WCP). Our algorithm needs only to solve one linear system of equation and performs one line search per iteration. Any accumulation point of the iteration sequence generated by our algorithm is a solution of WCP. Under suitable conditions, our algorithm has local quadratic convergence rate. Numerical experiments show the feasibility and efficiency of the algorithm.     

一种改进的密度核估计算法

密度核估计是解决统计问题中样本分布密度函数拟合的一类非参数统计方法,在经济、金融等领域有着重要的应用价值.密度核估计重点在于研究它的算法,使其估计值相对精确.本文提出了一种密度核估计的迭代方法,并通过算例与原有的密度核估计方法进行统计模拟比较,得出迭代后的值具有较好的拟合程度,充分验证了迭代方法的可行性与优越性.     

On the Existence of Fixed Points for Approximate Value Iteration and Temporal-Difference Learning

Approximate value iteration is a simple algorithm that combats the curse of dimensionality in dynamic programs by approximating iterates of the classical value iteration algorithm in a spirit reminiscent of statistical regression. Each iteration of this algorithm can be viewed as an application of a modified dynamic programming operator to the current iterate. The hope is that the iterates converge to a fixed point of this operator, which will then serve as a useful approximation of the optimal value function. In this paper, we show that, in general, the modified dynamic programming operator need not possess a fixed point; therefore, approximate value iteration should not be expected to converge. We then propose a variant of approximate value iteration for which the associated operator is guaranteed to possess at least one fixed point. This variant is motivated by studies of temporal-difference (TD) learning, and existence of fixed points implies here existence of stationary points for the ordinary differential equation approximated by a version of TD that incorporates exploration.     

A fast BIE iteration method for an arbitrary body in a flow of incompressible inviscid fluid

The paper is concerned with the new iteration algorithm to solve boundary integral equations arising in boundary value problems of mathematical physics. The stability of the algorithm is demonstrated on the problem of a flow around bodies placed in the incompressible inviscid fluid. With a discrete numerical treatment, we approximate the exact matrix by a certain Töeplitz one and then apply a fast algorithm for this matrix, on each iteration step. We illustrate the convergence of this iteration scheme by a number of numerical examples, both for hard and soft boundary conditions. It appears that the method is highly efficient for hard boundaries, being much less efficient for soft boundaries.     

求解不适定问题的快速Landweber迭代法

本文从一般迭代法的级数形式出发，将一般迭代法的每一步分解为矩阵计算和求解两步，并对其中的矩阵计算部分进行了修改，在此基础上提出了快速迭代法，最后通过数值实验验证了我们的算法不仅提高了计算速度，同时也大大减少了计算量，是一种效率很高的算法。     

A ROBUST SUPERLINEARLY CONVERGENT ALGORITHM FOR LINEARLY CONSTRAINED OPTIMIZATION PROBLEMS UNDER DEGENERACY

1.IntroductionTheproblemconsideredinthispaperiswhereX={xER"laTx5hi,jEI={l,.'.,m}},ajeR"(jEI)areallcolumn*ThisresearchissupportedbytheNationalNaturalSciencesFoundationofChinaandNaturalSciencesFoundationofHunanProvince.vectors,hiERI(j6I)areallscalars,andf:R"-- Risacontinuouslydifferentiablefunction.Weonlyconsiderinequalityconstraintsheresinceanyequalitycanbeexpressedastwoinequalities.Withoutassumingregularityofthelinearconstraints,thereisnotanydifficultyinextendingtheresultstothegenera…     

A Reference Direction Algorithm for Solving Multiple Objective Integer Linear Programming Problems

In this paper, we propose a reference direction approach and an interactive algorithm to solve the general multiple objective integer linear programming problem. At each iteration, only one mixed integer linear programming problem is solved to find an (weak) efficient solution. Each intermediate solution is integer. The decision maker has to provide only the reference point at each iteration. No special software is required to implement the proposed algorithm. The algorithm is illustrated with an example.     

一个解半正定规划问题的基于广义对数障碍函数的原始对偶内点算法

本文对经典对数障碍函数推广,给出了一个广义对数障碍函数.基于这个广义对数障碍函数设计了解半正定规划问题的原始-对偶内点算法.分析了该算法的复杂性,得到了一个理论迭代界,它与已有的基于经典对数障碍函数的算法的理论迭代界一致.同时,并给出了一个数值算例,阐明了函数的参数对算法运行时间的影响.     

A smoothing Newton method for the second-order cone complementarity problem

In this paper we introduce a new smoothing function and show that it is coercive under suitable assumptions. Based on this new function, we propose a smoothing Newton method for solving the second-order cone complementarity problem (SOCCP). The proposed algorithm solves only one linear system of equations and performs only one line search at each iteration. It is shown that any accumulation point of the iteration sequence generated by the proposed algorithm is a solution to the SOCCP. Furthermore, we prove that the generated sequence is bounded if the solution set of the SOCCP is nonempty and bounded. Under the assumption of nonsingularity, we establish the local quadratic convergence of the algorithm without the strict complementarity condition. Numerical results indicate that the proposed algorithm is promising.     

一种新修正的求解变分不等式的双次梯度外梯度算法

当可行集为一光滑凸函数的下水平集时, 本文提出一种修正的双次梯度外梯度算法(MTSEGA)用于求解Hilbert空间中单调且Lipschitz连续的变分不等式. MTSEGA在每步迭代过程中仅需计算向半空间的两次投影及一次映射的值. 在与已知算法相同的假设条件下, 证明了新算法产生的序列能弱收敛到相关问题的一个解.