A new hybrid method for solving global optimization problem

In this paper we present a new hybrid method, called the SASP method. The purpose of this method is the hybridization of the simulated annealing (SA) with the descent method, where we estimate the gradient using simultaneous perturbation. Firstly, the new hybrid method finds a local minimum using the descent method, then SA is executed in order to escape from the currently discovered local minimum to a better one, from which the descent method restarts a new local search, and so on until convergence.The new hybrid method can be widely applied to a class of global optimization problems for continuous functions with constraints. Experiments on 30 benchmark functions, including high dimensional functions, show that the new method is able to find near optimal solutions efficiently. In addition, its performance as a viable optimization method is demonstrated by comparing it with other existing algorithms. Numerical results improve the robustness and efficiency of the method presented.     

Numerical solution of second-order one-dimensional hyperbolic equation by exponential B-spline collocation method

In this paper, we propose a method based on collocation of exponential B-splines to obtain numerical solution of a nonlinear second-order one-dimensional hyperbolic equation subject to appropriate initial and Dirichlet boundary conditions. The method is a combination of B-spline collocation method in space and two-stage, second-order strong-stability-preserving Runge–Kutta method in time. The proposed method is shown to be unconditionally stable. The efficiency and accuracy of the method are successfully described by applying the method to a few test problems.     

双层规划问题的一种模式搜索Filter方法

双层规划在工程设计和经济管理中应用广泛,结合模式搜索方法和Filter方法提出了一种解决双层规划问题的算法—模式搜索Filter方法.算法以Filter法思想构造接受准则,以模式搜索提供迭代方向和步长,能够有效的解决一类双层规划问题.     

On convex optimization with linear constraints

In this paper, we propose an interior-point method for minimizing a convex function subject to linear constraints. Our method employs ideas from a previously studied method due to Fan and Nekooie in a different context. Under certain assumptions, we show that the proposed method has a fast rate of convergence. A numerical example is included to illustrate the method.     

一个解凸二次规划的预测-校正光滑化方法

本文为凸二次规划问题提出一个光滑型方法,它是Engelke和Kanzow提出的解线性规划的光滑化算法的推广。其主要思想是将二次规划的最优性K-T条件写成一个非线性非光滑方程组,并利用Newton型方法来解其光滑近似。本文的方法是预测-校正方法。在较弱的条件下,证明了算法的全局收敛性和超线性收敛性。     

Derivative-Free Filter Simulated Annealing Method for Constrained Continuous Global Optimization

In this paper, a simulated-annealing-based method called Filter Simulated Annealing (FSA) method is proposed to deal with the constrained global optimization problem. The considered problem is reformulated so as to take the form of optimizing two functions, the objective function and the constraint violation function. Then, the FSA method is applied to solve the reformulated problem. The FSA method invokes a multi-start diversification scheme in order to achieve an efficient exploration process. To deal with the considered problem, a filter-set-based procedure is built in the FSA structure. Finally, an intensification scheme is applied as a final stage of the proposed method in order to overcome the slow convergence of SA-based methods. The computational results obtained by the FSA method are promising and show a superior performance of the proposed method, which is a point-to-point method, against population-based methods.     

Finding roots of a real polynomial simultaneously by means of Bairstow's method

Aberth's method for finding the roots of a polynomial was shown to be robust. However, complex arithmetic is needed in this method even if the polynomial is real, because it starts with complex initial approximations. A novel method is proposed for real polynomials that does not require any complex arithmetic within iterations. It is based on the observation that Aberth's method is a systematic use of Newton's method. The analogous technique is then applied to Bairstow's procedure in the proposed method. As a result, the method needs half the computations per iteration than Aberth's method. Numerical experiments showed that the new method exhibited a competitive overall performance for the test polynomials.     

基于非线性尺度不变性的CCG法

１．引言 ＣＧ法对于变量个数很多的问题,是很有用的．１９７０年后它有了许多改进和发展,ＣＣＧ法以正定圆锥函数为基础［１］,它的一般方法是：设圆锥函数为 ２］其中： Ｖ＝ Ｖ（ｘ）＝１＋ ａＴｘ ≠ ０;, ｒ ∈Ｒ１为常量; ａ,ｇ ∈ Ｒｎ为常向量;ｘ ∈ Ｒｎ为变向量;Ａ∈Ｒｎ×ｎ为对称正定矩阵．算法［１］：预先给出初始近似点ｘ０∈ Ｒｎ及初始搜索方向 ｐ０;满足：其中“Ｉ”是单位矩阵, Ｖ０＝ Ｖ（ｘ０）＝ １＋ ａｔｘ０及记号“”是函数的梯度．迭代格式为： ｘｋ＋１＝ ｘｋ ＋λｋｐｋ,ｋ＝ ０,１,２,…（３…     

The Shell Method

<正>Here is another method for finding the volume of a solid of revolution.It's called the method of cylindrical shells or the shell method.For many problems,it's easier to apply than the disk method and washer method.So,what is a shell?A shell is a solid bounded by two concentric right circular cylinders(Figure 1).Some people also call it as a cylindrical shell.Shell method is always applied to a solid ob-     

Revision of distance minimization method for ranking of fuzzy numbers

Asady and Zendehnam employed “distance minimization” to ranking fuzzy numbers in Ref [1]. Then Abbasbandy and Hajjari in [2] found a problem of its. To overcome it problem, they proposed magnitude method to ranking fuzzy numbers. Unfortunately, their method can not to overcome this problem. In this paper, we want to indicate this problem and then propose a revise method of distance minimization method which can avoid problem for ranking fuzzy numbers. Since the revised method is based on the distance minimization method, it is easy to rank fuzzy numbers in a way similar to the original method.     

A Hybrid Algorithm for the Non-Guillotine Cutting Problem

In this article, a meta-heuristic method to solve the non-guillotine cutting stock problem is proposed. The method is based on a combination between the basic principles of the constructive and evolutive methods. With an adequate management of the parameters involved, the method allows regulation of the solution quality to computational effort relationship. This method is applied to a particular case of cutting problems, with which the computational behaviors is evaluated. In fact, 1000 instances of the problem have been classified according to their combinatorial degree and then the efficiency and robustness of the method have been tested. The final results conclude that the proposed method generates an average error close to 2.18% with respect to optimal solutions. It has also been verified that the method yields solutions for all of the instances examined; something that has not been achieved with an exact constructive method, which was also implemented. Comparison of the running times demonstrates the superiority of the proposed method as compared with the exact method.     

无约束优化问题的对角稀疏拟牛顿法

对无约束优化问题提出了对角稀疏拟牛顿法,该算法采用了Armijo非精确线性搜索,并在每次迭代中利用对角矩阵近似拟牛顿法中的校正矩阵,使计算搜索方向的存贮量和工作量明显减少,为大型无约束优化问题的求解提供了新的思路．在通常的假设条件下,证明了算法的全局收敛性,线性收敛速度并分析了超线性收敛特征。数值实验表明算法比共轭梯度法有效,适于求解大型无约束优化问题．     

Linearized ridge-path method for function minimization

A modification based on a linearization of a ridge-path optimization method is presented. The linearized ridge-path method is a nongradient, conjugate direction method which converges quadratically in half the number of search directions required for Powell's method of conjugate directions. The ridge-path method and its modification are compared with some basic algorithms, namely, univariate method, steepest descent method, Powell's conjugate direction method, conjugate gradient method, and variable-metric method. The assessment indicates that the ridge-path method, with modifications, could present a promising technique for optimization.This work was in partial fulfillment of the requirements for the MS degree of the first author at Cairo University, Cairo, Egypt. The authors would like to acknowledge the helpful and constructive suggestions of the reviewer.     

The existence of symplectic general linear methods

We derive a criterion that any general linear method must satisfy if it is symplectic. It is shown, by considering the method over several steps, that the satisfaction of this condition leads to a reducibility in the method. Linking the symplectic criterion here to that for Runge–Kutta methods, we demonstrate that a general linear method is symplectic only if it can be reduced to a method with a single input value.      

Hybrid Newton-Type Method for a Class of Semismooth Equations

In this paper, we present a hybrid method for the solution of a class of composite semismooth equations encountered frequently in applications. The method is obtained by combining a generalized finite-difference Newton method to an inexpensive direct search method. We prove that, under standard assumptions, the method is globally convergent with a local rate of convergence which is superlinear or quadratic. We report also several numerical results obtained applying the method to suitable reformulations of well-known nonlinear complementarity problems.     

关于薄板的无网格局部边界积分方程方法中的友解

无网格局部边界积分方程方法是最近发展起来的一种新的数值方法,这种方法综合了伽辽金有限元、边界元和无单元伽辽金法的优点,是一种具有广阔应用前景的、真正的无网格方法．把无网格局部边界积分方程方法应用于求解薄板问题,给出了薄板无网格局部边界积分方程方法所需要的友解及其全部公式．     

SOLVING TRUST REGION PROBLEM IN LARGE SCALEOPTIMIZATION

1.IntroductionLetHbeagivennxnsymmetricpositivesemidefinitematrixandcER".Inthispaperweconsiderthefollowingquadraticprogrammingwithasimplequadraticalconstraint1r--XTH. CTX=min2(1)s.tIlxlls5a,wheretheparameteraisprescribed.Thisproblemoccursfrequentlyintrustrationmethodforunconstrainedoptimization[11.Anumberofapproachesforsolving(1)havebeenproposedintheliterature[2,3,6,12--16].OnetechniqueistoapproximateaLagrangemultiplierAbyNewton'smethod.Theapproximationofthisparametermaybequitedelicate,ho…     

乘子方法中的参数选择

Di Pillo和Grippo提出的含参数C〉0的增广Lagrangian函数中，使用了最大函数，该函数可能在无穷多个点处不可微．为了克服这个问题，濮定国在2004年提出了一类带新的NCP函数的乘子法．该方法在增广Lagrangian函数和原问题之间存在很好的等价性；同时该方法具有全局收敛性，且在适当假设下，具有超线性收敛率．但是在该方法中，要求参数C充分大．为了实现算法及提高算法效率，本文给出了一个有效选择参数C的方法．     

线性规划基线算法的基本概念

１．运算表格线性规划的基线算法是单纯形法（基点算法）的发展,因为每张运算表格对应着一条基线而得名．它象单纯形法一样好学易用,操作简便,而解题速度比单纯形法快．考虑标准型线性规划问题（ＬＰ）：：其中ｃ,ｘｅＲ"＋",Ａ是。ｘ（佩十。）矩阵,ｂｅＲ"。是（ＬＰ）的维数,。是约束个数．Ｘ＝｛ＸＥＲ""叫ＡＸ＝ｂ,Ｘ三０｝是（＊利的可行集．Ｘ是一个多面凸集．本文假定Ｃ４０．并且原点不是最优解．把Ｘ看作参数．方程组０．】Ｘ＝０,】的系数表称为母表（表１）．恒假设矩阵０－１－＼Ａｊ＼ｈｉ一"-一'-－"－"'一'-"-一"…     

A Runge–Kutta type modified Landweber method for nonlinear ill-posed operator equations

In this paper, we investigate the convergence behavior of a Runge–Kutta type modified Landweber method for nonlinear ill-posed operator equations. In order to improve the stability and convergence of the Landweber iteration, a 2-stage Gauss-type Runge–Kutta method is applied to the continuous analogy of the modified Landweber method, to give a new modified Landweber method, called R–K type modified Landweber method. Under some appropriate conditions, we prove the convergence of the proposed method. We conclude with a numerical example confirming the theoretical results, including comparisons to the modified Landweber iteration.