求解结构型单调变分不等式的改进的邻近类分解方法

邻近类分解方法首先是由Chen和Teboulle（Math. Programming,1994,64(1):81-101）提出用来求解凸的极小化问题．在此基础上,该文提出一种新方法求解具有分离结构的单调变分不等式．其主要优点在于放松了算法中对某些参数的限制,使得新方法更加便于计算．在和原分解方法相同的假设下,可以证明新方法是全局收敛的．     

Robin型离散Schwarz波形松弛算法的收敛性分析

Schwarz波形松弛(Schwarz waveform relaxation,SWR)是一种新型区域分解算法,是当今并行计算研究领域的焦点之一,但针对该算法的收敛性分析基本上都停留在时空连续层面.从实际计算角度看,分析离散SWR算法的收敛性更重要.本文考虑SWR研究领域中非常流行的Robin型人工边界条件,分析时空离散参数t和x、模型参数等因素对算法收敛速度的影响.Robin型人工边界条件中含有一个自由参数p,可以用来优化算法的收敛速度,但最优参数的选取却需要求解一个非常复杂的极小-极大问题.本文对该极小-极大问题进行深入分析,给出最优参数的计算方法.本文给出的数值实验结果表明所获最优参数具有以下优点:(1)相比连续情形下所获最优参数,利用离散情形下获得的参数可以进一步提高Robin型SWR算法在实际计算中的收敛速度,当固定t或x而令另一个趋于零时,利用离散情形下所获参数可以使算法的收敛速度具有鲁棒性(即收敛速度不随离散参数的减小而持续变慢).(2)相比连续情形下所获收敛速度估计,离散情形下获得的收敛速度估计可以更加准确地预测算法的实际收敛速度.     

关于解极大相关问题P-SOR算法的收敛性

对求解极大相关问题的P-SOR方法的收敛性做了进一步研究.得到了一些新的收敛条件.为了提高收敛到全局最大解的可能性,提出了一种新的初始向量选择策略.给出了P-SOR算法的对称形式(P-SSOR).还给出了一种算法精化策略.最后,用数值例子说明新方法的有效性.     

变分同伦摄动迭代法求解抛物型方程反问题中的控制参数北大核心CSCD

变分同伦摄动迭代法是结合变分迭代法和同伦摄动法而产生的新方法,被应用于求解含有未知参数的线性抛物型方程反问题.通过该方法,可以快速得到收敛于反问题精确解的收敛序列.本文通过一些实例,来验证说明该方法的高效性和可靠性.     

变分同伦摄动迭代法求解抛物型方程反问题中的控制参数

变分同伦摄动迭代法是结合变分迭代法和同伦摄动法而产生的新方法,被应用于求解含有未知参数的线性抛物型方程反问题.通过该方法,可以快速得到收敛于反问题精确解的收敛序列.本文通过一些实例,来验证说明该方法的高效性和可靠性.     

带学习效应的两台平行机时间表长问题

研究机器带学习效应, 目标函数为时间表长的两台平行机排序问题, 问题是NP-难的. 首先建立了求解该问题最优解的整数规划模型. 其次, 基于模拟退火算法给出了该问题的近似算法SA, 并证明了该算法依概率1 全局收敛到最优解. 最后, 通过数值模拟对所提出的算法进行了性能分析. 数值模拟结果表明, 近似算法SA可以达到最优值的99%, 准确度高, 算法较有效.     

有向网络上随机—闲聊设置下的一个动量加速算法

本文考虑一个分布式优化问题,其中整个网络上智能体之间的交互可能会发生链路故障,并在随机—闲聊设置下提出了一个有向网络上的动量加速算法.在目标函数是强凸且光滑的假设下,从理论上证明了所提出的算法可以线性收敛到精确解.由于使用了重球动量项,所提出的算法可以更快地收敛到精确解.数值结果表明,与现有的分布式算法相比,该算法能够更快地收敛到精确解,特别是对于病态问题.     

基于二进制编码非洲野狗算法的TSP问题研究

针对非洲野狗算法求解优化问题时全局性收敛不强的特点,对该算法进行改进,提出了改进的非洲野狗算法,结合二进制编码设计了求解离散优化问题的二进制编码非洲野狗算法,并将该算法应用于求解TSP问题并与其他算法做对比分析.研究结果显示,求解TSP问题时二进制编码非洲野狗算法求解精度更高,收敛速度更快.     

两类解非线性约束问题的超记忆可行方向法

本文将无约束超记忆梯度法推广到非线性不等式约束优化问题上来,给出了两类形式很一般的超记忆可行方向法,并在非退化及连续可微等较弱的假设下证明了其全局收敛性.适当选取算法中的参量及记忆方向,不仅可得到一些已知的方法及新方法,而且还可能加快算法的收敛速度.     

等几何分析的多重网格共轭梯度法

提高NURBS基函数阶数可以提高等几何分析的精度,同时也会降低多重网格迭代收敛速度.将共轭梯度法与多重网格方法相结合,提出了一种提高收敛速度的方法,该方法用共轭梯度法作为基础迭代算法,用多重网格进行预处理.对Poisson(泊松)方程分别用多重网格方法和多重网格共轭梯度法进行了求解,计算结果表明:等几何分析中采用高阶NURBS基函数处理三维问题时,多重网格共轭梯度法比多重网格法的收敛速度更快.     

A fast and robust unconstrained optimization method requiring minimum storage

This paper describes a new unconstrained optimisation procedure employing conjugate directions and requiring only threen-dimensional vectors. The method has been tested for computational efficiency and stability on a large set of test functions and compared with numerical data of other major methods. Results show that the method possesses strong superiority over other existing conjugate gradient methods on all problems and can out-perform or is at least as efficient as quasi-Newton methods on many tested problems.     

RC_Link: Genetic linkage analysis using Bayesian networks

Genetic linkage analysis is a statistical method for mapping genes onto chromosomes, and is useful for detecting and predicting diseases. One of its current limitations is the computational complexity of the problems of interest. This research presents methods for mapping genetic linkage problems as Bayesian networks and then addresses novel techniques for making the problems more tractable. The result is a new tool for solving these problems called RC_Link, which in many cases is orders of magnitude faster than existing tools.     

Mehar’s methods for fuzzy assignment problems with restrictions

In this paper, limitations of existing methods [5, 11] for solving fuzzy assignment problems (FAPs) are pointed out. In order to overcome the limitations of existing methods, two new methods named Mehar’s methods are proposed. To show the advantages of Mehar’s methods over existing methods, some FAPs are solved. The Mehar’s methods can solve the problems solved by existing methods as well as those which cannot be solved by existing methods.     

A New Method to Find the Unique Fuzzy Optimal Value of Fuzzy Linear Programming Problems

In this paper, shortcomings and limitations of the existing methods for solving fuzzy linear programming (FLP) problems are pointed out. To overcome the limitations as well as to resolve the shortcomings, a new method is proposed for solving FLP problems. To show the advantage of the proposed method over existing methods, a FLP problem is solved by the existing methods as well as the proposed method, and the obtained results are compared.     

Application of classical transportation methods to find the fuzzy optimal solution of fuzzy transportation problems

To the best of our knowledge till now there is no method in the literature to find the exact fuzzy optimal solution of unbalanced fully fuzzy transportation problems. In this paper, the shortcomings and limitations of some of the existing methods for solving the problems are pointed out and to overcome these shortcomings and limitations, two new methods are proposed to find the exact fuzzy optimal solution of unbalanced fuzzy transportation problems by representing all the parameters as LR flat fuzzy numbers. To show the advantages of the proposed methods over existing methods, a fully fuzzy transportation problem which may not be solved by using any of the existing methods, is solved by using the proposed methods and by comparing the results, obtained by using the existing methods and proposed methods. It is shown that it is better to use proposed methods as compared to existing methods.     

How to solve a design centering problem

This work considers the problem of design centering. Geometrically, this can be thought of as inscribing one shape in another. Theoretical approaches and reformulations from the literature are reviewed; many of these are inspired by the literature on generalized semi-infinite programming, a generalization of design centering. However, the motivation for this work relates more to engineering applications of robust design. Consequently, the focus is on specific forms of design spaces (inscribed shapes) and the case when the constraints of the problem may be implicitly defined, such as by the solution of a system of differential equations. This causes issues for many existing approaches, and so this work proposes two restriction-based approaches for solving robust design problems that are applicable to engineering problems. Another feasible-point method from the literature is investigated as well. The details of the numerical implementations of all these methods are discussed. The discussion of these implementations in the particular setting of robust design in engineering problems is new.     

A new load-dependent Ritz vector method for structural dynamics analyses: quasi-static Ritz vectors

Existing load-dependent Ritz vector (LDRV) methods employ static recurrence procedures to generate the Ritz vectors. As such, these vector methods are best suited for low-frequency problems. For higher-frequency problems, the existing methods may engender large sets of Ritz vectors, which significantly reduces the methods’ efficiency. A new algorithm is presented for LDRV generation using a quasi-static recurrence procedure, denoted as the quasi-static Ritz vector (QSRV) method. A tuning parameter, designated as the centering frequency, controls the behavior of the QSRV approach, enabling the new method to improve upon existing LDRV methods for particular frequency ranges of interest. Compared with existing LDRV methods, the QSRV method is more efficient (in terms of the number of Ritz vectors), more accurate (in terms of response errors), and more stable (in terms of orthogonality). Numerical examples are provided to illustrate the accuracy, efficiency and generality of the proposed method.     

A family of optimal fourth-order methods for multiple roots of nonlinear equations

Newton-Raphson method has always remained as the widely used method for finding simple and multiple roots of nonlinear equations. In the past years, many new methods have been introduced for finding multiple zeros that involve the use of weight function in the second step, thereby, increasing the order of convergence and giving a flexibility to generate a family of methods satisfying some underlying conditions. However, in almost all the schemes developed over the past, the usual way is to use Newton-type method at the first step. In this paper, we present a new two-step optimal fourth-order family of methods for multiple roots (m > 1). The proposed iterative family has the flexibility of choice at both steps. The development of the scheme is based on using weight functions. The first step can not only recapture Newton's method for multiple roots as special case but is also capable of defining new choices of first step. A stability analysis of some particular cases is also given to explain the dynamical behavior of the new methods around the multiple roots and decide the best values of the free parameters involved. Finally, we compare our methods with the existing schemes of the same order with a real life application as well as standard test problems. From the numerical results, we find that our methods can be considered as a better alternative for the existing procedures of same order.     

Robust multicategory support vector machines using difference convex algorithm

The support vector machine (SVM) is one of the most popular classification methods in the machine learning literature. Binary SVM methods have been extensively studied, and have achieved many successes in various disciplines. However, generalization to multicategory SVM (MSVM) methods can be very challenging. Many existing methods estimate k functions for k classes with an explicit sum-to-zero constraint. It was shown recently that such a formulation can be suboptimal. Moreover, many existing MSVMs are not Fisher consistent, or do not take into account the effect of outliers. In this paper, we focus on classification in the angle-based framework, which is free of the explicit sum-to-zero constraint, hence more efficient, and propose two robust MSVM methods using truncated hinge loss functions. We show that our new classifiers can enjoy Fisher consistency, and simultaneously alleviate the impact of outliers to achieve more stable classification performance. To implement our proposed classifiers, we employ the difference convex algorithm for efficient computation. Theoretical and numerical results obtained indicate that for problems with potential outliers, our robust angle-based MSVMs can be very competitive among existing methods.     

Applications of fuzzy linear programming with generalized LR flat fuzzy parameters

In this paper, the limitations of existing methods to solve the problems of fuzzy assignment, fuzzy travelling salesman and fuzzy generalized assignment are pointed out. All these problems can be formulated in linear programming problems wherein the decision variables are represented by real numbers and other parameters are represented by fuzzy numbers. To overcome the limitations of existing methods, a new method is proposed. The advantage of proposed method over existing methods is demonstrated by solving the problems mentioned above which can or cannot be solved by using the existing methods.