Reciprocal Function Method for Cauchy Problems with First-Order Poles

Doklady Mathematics - For the numerical solution of the Cauchy problem with multiple poles, we propose a reciprocal function method. In the case of first-order poles, it makes it possible to...     

Modified descent-projection method for solving variational inequalities

In this paper, we propose a modified descent-projection method for solving variational inequalities. The method makes use of a descent direction to produce the new iterate and can be viewed as an improvement of the descent-projection method by using a new step size. Under certain conditions, the global convergence of the proposed method is proved. In order to demonstrate the efficiency of the proposed method, we provide numerical results for a traffic equilibrium problems.     

LMI Optimization Approach to Observer-Based Controller Design of Uncertain Time-Delay Systems via Delayed Feedback

In this paper, we propose a design method of an observer-based controller for uncertain time-delay systems by delayed feedback. Based on the Lyapunov method, an LMI (linear matrix inequality) criterion is derived to design an observer-based controller which makes the system stable. A numerical example is included to illustrate the design procedure.     

Monitoring of dynamic processes by rectangular hybrid automata

In this paper we develop a method of monitoring dynamic processes based on rectangular hybrid automats. This method takes into account the behavior of the system and the evolution of its parameters. A failure during the execution of the process can lead to a dysfunctional state in the system.The monitoring system, we propose, makes it possible to detect this state of dysfunction as soon as possible thanks to the reachability analysis.     

改进的函数系数自回归建模方法对上海股市实证分析

函数系数自回归模型(FAR)是一类更具有适应性的模型。本文利用函数系数自回归模型对上海股市日收益率进行建模及短期预测,改进现有建模对带宽、模型的依赖变量以及阶数确定方法。并与上海股市日收益率的自回归模型结果进行了比较,结果表明改进的函数系数模型具有很好的预测能力。     

Bounds on entanglement dimensions and quantum graph parameters via noncommutative polynomial optimization

This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery using a random subset of entries observed with additive noise under general non-uniform and unknown sampling distributions. This method significantly relaxes the uniform sampling assumption imposed for the widely used nuclear-norm penalized approach, and makes low-rank matrix recovery feasible in more practical settings. Theoretically, we prove that the proposed estimator achieves fast rates of convergence under different settings. Computationally, we propose an alternating direction method of multipliers algorithm to efficiently compute the estimator, which bridges a gap between theory and practice of machine learning methods with max-norm regularization. Further, we provide thorough numerical studies to evaluate the proposed method using both simulated and real datasets.     

一种可用于生产效率评价的灰靶评估算法

本文在分析和比较了DEA和灰靶评估两种方法之后，给出一种可用于生产效率评价的灰靶评估算法。该算法由于运用了DEA方法中的“生产效率”概念，弥补了灰靶评估算法不能对不同的被评价单元进行效率评价的不足，从而拓宽了灰靶评估算法的应用背景。文章最后给出实例分析。     

Local linear kernel estimation of the discontinuous regression function

We address the problems of estimating the discontinuous regression function and also its jump points. We propose a method in two steps: we first estimate the jumps and finally the regression function is estimated by an adapted version of a local linear smoother which makes use of the estimated jumps. The practical performance of the proposed method is evaluated by using simulation studies and an application to a real-life problem.     

多成份流体计算

本文对可压缩多成份流体计算问题提出一种守恒的捕捉算法．我们根据这类多成份流体本身的物理性质，建立了新的计算方法，在计算中控制了各成份流体之间的能量交换，从而使得算法守恒且无震荡．有效的数值试验表明，该算法可求解可压缩多成份流问题，并且能在整个计算过程中保持守恒量的守恒．     

Key predistribution schemes for distributed sensor networks via block designs

Key predistribution schemes for distributed sensor networks have received significant attention in the recent literature. In this paper we propose a new construction method for these schemes based on combinations of duals of standard block designs. Our method is a broad spectrum one which works for any intersection threshold. By varying the initial designs, we can generate various schemes and this makes the method quite flexible. We also obtain explicit algebraic expressions for the metrics for local connectivity and resiliency. These schemes are quite efficient with regard to connectivity and resiliency and at the same time they allow a straightforward shared-key discovery.     

Global convergence analysis of the aggregate constraint homotopy method for nonlinear programming problems with both inequality and equality constraints

In this paper, we construct appropriate aggregate mappings and a new aggregate constraint homotopy (ACH) equation by converting equality constraints to inequality constraints and introducing two variable parameters. Then, we propose an ACH method for nonlinear programming problems with inequality and equality constraints. Under suitable conditions, we obtain the global convergence of this ACH method, which makes us prove the existence of a bounded smooth path that connects a given point to a Karush–Kuhn–Tucker point of nonlinear programming problems. The numerical tracking of this path can lead to an implementable globally convergent algorithm. A numerical procedure is given to implement the proposed ACH method, and the computational results are reported.     

Interior-Point Lagrangian Decomposition Method for Separable Convex Optimization

In this paper, we propose a distributed algorithm for solving large-scale separable convex problems using Lagrangian dual decomposition and the interior-point framework. By adding self-concordant barrier terms to the ordinary Lagrangian, we prove under mild assumptions that the corresponding family of augmented dual functions is self-concordant. This makes it possible to efficiently use the Newton method for tracing the central path. We show that the new algorithm is globally convergent and highly parallelizable and thus it is suitable for solving large-scale separable convex problems.     

A one-parametric class of smoothing functions and an improved regularization Newton method for the NCP

In this paper, we introduce a one-parametric class of smoothing functions, which enjoys some favourable properties and includes two famous smoothing functions as special cases. Based on this class of smoothing functions, we propose a regularization Newton method for solving the non-linear complementarity problem. The main feature of the proposed method is that it uses a perturbed Newton equation to obtain the direction. This not only allows our method to have global and local quadratic convergences without strict complementarity conditions, but also makes the regularization parameter converge to zero globally Q-linearly. In addition, we use a new non-monotone line search scheme to obtain the step size. Some numerical results are reported which confirm the good theoretical properties of the proposed method.     

A Modified Alternating Direction Method for Variational Inequality Problems

The alternating direction method is an attractive method for solving large-scale variational inequality problems whenever the subproblems can be solved efficiently. However, the subproblems are still variational inequality problems, which are as structurally difficult to solve as the original one. To overcome this disadvantage, in this paper we propose a new alternating direction method for solving a class of nonlinear monotone variational inequality problems. In each iteration the method just makes an orthogonal projection to a simple set and some function evaluations. We report some preliminary computational results to illustrate the efficiency of the method. Accepted 4 May 2001. Online publication 19 October, 2001.     

推广AS-GN混合共轭梯度算法

本文提出了一种求解无约束优化问题的新算法,使Touati-Ahmed, Storey提出的混合共轭梯度法(以下简称AS)和Gilbert, Nocedal提出的混合共轭梯度法(以下简称GN)成为新算法在精确线性搜索下的特例.通过构造新的$\beta_{k}$计算公式,新算法自然满足下降性条件,且这个性质与线性搜索和目标函数的凸性均无关.在一般的条件下,我们证明了新算法的全局收敛性.数值结果表明该算法对测试函数是有效的.     

The problem of processing time series: Extending possibilities of the local approximation method using singular spectrum analysis

We present algorithms for singular spectrum analysis and local approximation methods used to extrapolate time series. We analyze the advantages and disadvantages of these methods and consider the peculiarities of applying them to various systems. Based on this analysis, we propose a generalization of the local approximation method that makes it suitable for forecasting very noisy time series. We present the results of numerical simulations illustrating the possibilities of the proposed method.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 1, pp. 148–159, January, 2005.     

一般分布区间型符号数据的SOM聚类方法

区间型符号数据是一种重要的符号数据类型,现有文献往往假设区间内的点数据服从均匀分布,导致其应用的局限性。本文基于一般分布的假设,给出了一般分布区间型符号数据的扩展的Hausdorff距离度量,基于此提出了一般分布的区间型符号数据的SOM聚类算法。随机模拟试验的结果表明,基于本文提出的基于扩展的Hausdorff距离度量的SOM聚类算法的有效性优于基于传统Hausdorff距离度量的SOM聚类算法和基于μσ距离度量的SOM聚类算法。最后将文中方法应用于气象数据的聚类分析,示例文中方法的应用步骤与可操作性,并进一步评价文中方法在解决实际问题中的有效性。     

A modification of the stochastic ruler method for discrete stochastic optimization

We propose a modified stochastic ruler method for finding a global optimal solution to a discrete optimization problem in which the objective function cannot be evaluated analytically but has to be estimated or measured. Our method generates a Markov chain sequence taking values in the feasible set of the underlying discrete optimization problem; it uses the number of visits this sequence makes to the different states to estimate the optimal solution. We show that our method is guaranteed to converge almost surely (a.s.) to the set of global optimal solutions. Then, we show how our method can be used for solving discrete optimization problems where the objective function values are estimated using either transient or steady-state simulation. Finally, we provide some numerical results to check the validity of our method and compare its performance with that of the original stochastic ruler method.     

Practical estimation of a splitting parameter for a spectral method for the ternary Cahn–Hilliard system with a logarithmic free energy

We propose a practical estimation of a splitting parameter for a spectral method for the ternary Cahn–Hilliard system with a logarithmic free energy. We use Eyre's convex splitting scheme for the time discretization and a Fourier spectral method for the space variables. Given an absolute temperature, we find composition values that make the total free energy be minimum. Then, we find the splitting parameter value that makes the two split homogeneous free energies be convex on the neighborhood of the local minimum concentrations. For general use, we also propose a sixth‐order polynomial approximation of the minimum concentration and derive a useful formula for the practical estimation of the splitting parameter in terms of the absolute temperature. The numerical tests are phase separation and total energy decrease with different temperature values. The linear stability analysis shows a good agreement between the exact and numerical solutions with an optimal value s. Various computational experiments confirm that the proposed splitting parameter estimation gives stable numerical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Inexact Operator Splitting Methods with Selfadaptive Strategy for Variational Inequality Problems

The Peaceman-Rachford and Douglas-Rachford operator splitting methods are advantageous for solving variational inequality problems, since they attack the original problems via solving a sequence of systems of smooth equations, which are much easier to solve than the variational inequalities. However, solving the subproblems exactly may be prohibitively difficult or even impossible. In this paper, we propose an inexact operator splitting method, where the subproblems are solved approximately with some relative error tolerance. Another contribution is that we adjust the scalar parameter automatically at each iteration and the adjustment parameter can be a positive constant, which makes the methods more practical and efficient. We prove the convergence of the method and present some preliminary computational results, showing that the proposed method is promising. This work was supported by the NSFC grant 10501024.