Compound modification of globoidal worm drive with variable parameters

The meshing theory is built for the globoidal worm drive systematically. Several modification parameters, including the center distance, the transmitting ratio and the height of the cutter frame, are taken into account concurrently and they are all variable. Many types of modification in the foregoing study can be viewed as the special cases of this work. A new method is proposed to obtain the velocity ratio modification function. The height modification function is recommended to adopt a linear function, whose coefficients may be determined by the trial method. The meshing function of the worm pair is deduced by virtue of the vector rotation approach. In the case of the modification with single constant parameter, the classification standard of the drive type is proved strictly. The computing methods of the contact zone, the contact line, and the instantaneous meshing point are expounded explicitly. The reason why a globoidal worm drive can implement the double-line contact between the teeth is uncovered clearly. The reason why a modified globoidal worm gearing can shun the curvature interference is discovered. The comparative researches on the mesh characters of the diverse modified drives are implemented adequately. Some kinds of the modified drive, containing the compound modified drive with variable parameters, are recommended to be utilized in practice for the excellent mesh performances.     

一类修改的带NCP函数信赖域滤子算法

本文针对非线性规划给出了一种修改的带NCP函数的信赖域滤子SQP算法,主要的修改之处是用NCP函数替代了滤子中约束违反度函数,而且进一步证明了这种修改的算法同样具有全局收敛性.     

A COLUMN-SECANT UPDATE TECHNIQUE FOR SOLVING SYSTEM OF NONLINEAR EQUATIONS

In this paper,we present a column-secant modification of the SCC method,which is called the CSSCC method.The CSSCC method uses function values more efficiently than the SCC method,and it is shown that the CSSCC method has better local q-convergence and r-convergence rates than the SCC method.The numerical results show that the CSSCC method is competitive with some well known methods for some standard test problems.     

A modified Newton method with cubic convergence: the multivariate case

Recently, a modification of the Newton method for finding a zero of a univariate function with local cubic convergence has been introduced. Here, we extend this modification to the multi-dimensional case, i.e., we introduce a modified Newton method for vector functions that converges locally cubically, without the need to compute higher derivatives. The case of multiple roots is not treated. Per iteration the method requires one evaluation of the function vector and solving two linear systems with the Jacobian as coefficient matrix, where the Jacobian has to be evaluated twice. Since the additional computational effort is nearly that of an additional Newton step, the proposed method is useful especially in difficult cases where the number of iterations can be reduced by a factor of two in comparison to the Newton method. This much better convergence is indeed possible as shown by a numerical example. Also, the modified Newton method can be advantageous in cases where the evaluation of the function is more expensive than solving a linear system with the Jacobian as coefficient matrix. An example for this is given where numerical quadrature is involved. Finally, we discuss shortly possible extensions of the method to make it globally convergent.     

A class of difference ABS-type algorithms for a nonlinear system of equations

In this paper we give a class of algorithms for solving nonlinear algebraic equations using difference approximations of derivatives. The class is a modification of the original ABS class with the advantage of requiring less function evaluations. Special cases include the methods of Brown and Brent and the discretized Newton method, which is formulated in a way requiring fewer function evaluations per iteration.     

A sufficient descent LS conjugate gradient method for unconstrained optimization problems

In this paper, we make a modification to the Liu-Storey (LS) conjugate gradient method and propose a descent LS method. The method can generate sufficient descent directions for the objective function. This property is independent of the line search used. We prove that the modified LS method is globally convergent with the strong Wolfe line search. The numerical results show that the proposed descent LS method is efficient for the unconstrained problems in the CUTEr library.     

A TRUST REGION-TYPE METHOD FOR SOLVINGMONOTONE VARIATIONAL INEQUALITY

1.IntroductionLetSbeanonemptyclosedconvexsubsetofR"andletF:R"-R"beacontinuousmapping.ThevariatiollalillequalityproblemFindx*6Ssuchthat(F(x*),x--x*)20forallxeS(VIP)iswidelyusedtostudyvariousequilibriummodelsarisingilleconomic,operatiollsresearch,transportatiollandregionalsciellces[2'3I?where(.,.)dellotestheinnerproductinR".Manyiterativemethodsfor(VIP)havebeendeveloped,forexample,projectionmethods[7ts],thenonlinearJacobimethod[5],thesuccessiveoverrelaxation.ethod[9]andgeneralizedgradient.…     

A Sixth-order P-stable Symmetric Multistep Method for Periodic Initial-value Problems of Second-order Differential Equations

A sixth-order P-stable symmetric multistep method for periodicinitial-value problem y = f(x, y) is suggested. It requiresthree function evaluations per iteration. The method can beconsidered as a stabilized modification of Lambert and Watson'ssixth-order implicit method which has a finite interval of periodicity.The method is illustrated for three numerical examples.     

Progressive global random search of continuous functions

A sequential random search method for the global minimization of a continuous function is proposed. The algorithm gradually concentrates the random search effort on areas neighboring the global minima. A modification is included for the case that the function cannot be exactly evaluated. The global convergence and the asymptotical optimality of the sequential sampling procedure are proved for both the stochastic and deterministic optimization problem.The research is sponsored in part by the Air Force under Grant AFOSR-72-2371.     

一个阶为2+\sqrt{6}的Newton改进算法

针对非线性方程求单根问题,提出了一种新的Newton预测-校正格式.通过每步迭代增加计算一个函数值和一阶导数值,使得每步迭代需要估计两个函数值和两个一阶导数值.与标准的Newton算法的二阶收敛速度相比,新算法具有更高阶的收敛速度2+\sqrt{6}.通过测试函数对新算法进行测试, 与相关算法比较,表明算法在迭代次数、运算时间及最优值方面都具有较明显的优势. 最后,将这种新格式推广到多维向量值函数, 采用泰勒公式证明了其收敛性,并给出了两个二维算例来验证其收敛的有效性.     

结合修正Curry-Altman步长搜索一个新的共轭梯度算法的收敛性

Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameter in the search directions. In this note, conditions are given on the parameter in the conjugate gradient directions to ensure the descent property of the search directions. Global convergence of such a class of methods is discussed. It is shown that, using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continuously differentiable function with a modification of the Curry-Altman‘s step-size rule and a bounded level set. Combining PR method with our new method, PR method is modified to have global convergence property.Numerical experiments show that the new methods are efficient by comparing with FR conjugate gradient method.     

An Imputation Method for Missing Data in Compositional Based on Epanechnikov Kernel

Kernel function method has been successfully used for the estimation of a variety of function. By using the kernel function theory, an imputation method based on Epanechnikov kernel and its modification were proposed to solve the problem that missing data in compositional caused the failures of existing statistical methods and the k-nearest imputation didn't consider the different contributions of the k nearest samples when it used them to estimated the missing data. The experimental results illustrate that the modified imputation method based on Epanechnikov kernel get a more accurate estimation than k-nearest imputation for compositional data.     

A numerically stable optimization method based on A homogeneous function

An improved version of an unconstrained optimization algorithm based upon a homogeneous function is presented. The method is numerically stable and uses the Bartels—Golub factorization instead of Householder's modification formula. Several numerical tests indicate that the proposed method is robust and very efficient.     

Heuristic Methods for Linear Multiplicative Programming

The linear multiplicative programming is the minimization of the product of affine functions over a polyhedral set. The problem with two affine functions reduces to a parametric linear program and can be solved efficiently. For the objective function with more than two affine functions multiplied, no efficient algorithms that solve the problem to optimality have been proposed, however Benson and Boger have proposed a heuristic algorithm that exploits links of the problem with concave minimization and multicriteria optimization. We will propose a heuristic method for the problem as well as its modification to enhance the accuracy of approximation. Computational experiments demonstrate that the method and its modification solve randomly generated problems within a few percent of relative error.     

Existence and location results for sign-changing solutions for three-point boundary value problems using Leray-Schauder degree

In this paper, by using the modification function technique and the Leray-Schauder degree method some existence and multiplicity results for sign- changing solutions of certain three-point boundary value problems are obtained. The main result of this paper is an improvement on a former existence result for sign-changing solutions of certain three-point boundary value problems.     

Existence and location results for sign-changing solutions for three-point boundary value problems using Leray-Schauder degree

In this paper, by using the modification function technique and the Leray-Schauder degree method some existence and multiplicity results for sign- changing solutions of certain three-point boundary value problems are obtained. The main result of this paper is an improvement on a former existence result for sign-changing solutions of certain three-point boundary value problems.     

A modified concave simplex algorithm for geometric programming

An algorithm for solving posynomial geometric programs is presented. The algorithm uses a modification of the concave simplex method to solve the dual program which has a nondifferentiable objective function. The method permits simultaneous changes in certain blocks of dual variables. A convergence proof follows from the convergence proof of the concave simplex method. Some computational results on problems with up to forty degrees of difficulty are included.     

How to increase convergence order of the Newton method to 2 × m?

We present a simple and effective scheme for forming iterative methods of various convergence orders. In this scheme, methods of various convergence orders, such as four, six, eight and ten, are formed through a modest modification of the classical Newton method. Since the scheme considered is a simple modification of the Newton method, it can be easily implemented in existing software packages, which is also suggested by the presented pseudocodes. Finally some problems are solved, to very high precision, through the proposed scheme. Numerical work suggests that the presented scheme requires less number of function evaluations for convergence and it may be suitable in high precision computing.     

A modification of the DIRECT method for Lipschitz global optimization for a symmetric function

In this paper, we consider a global optimization problem for a symmetric Lipschitz continuous function. An efficient modification of the well-known DIRECT (DIviding RECTangles) method called SymDIRECT is proposed for solving this problem. The method is illustrated and tested on several standard test functions. The application of this method to solving complex center-based clustering problems for the data having only one feature is particularly presented.     

On the Global Convergence of a Modified Augmented Lagrangian Linesearch Interior-Point Newton Method for Nonlinear Programming

We consider a linesearch globalization of the local primal-dual interior-point Newton method for nonlinear programming introduced by El-Bakry, Tapia, Tsuchiya, and Zhang. The linesearch uses a new merit function that incorporates a modification of the standard augmented Lagrangian function and a weak notion of centrality. We establish a global convergence theory and present promising numerical experimentation.