求解变分不等式的非单调混合Newton算法

本文运用广义D-间隙函数可以将变分不等式问题转化为一个无约束最优化问题,即极小化广义D-间隙函数的一般形式gαβ,基于非单调线搜索技术提出一种非单调混合Newton算法,并给出了算法的全局收敛性分析.在适当条件下,证明了算法具有全局二次收敛性.同时在映射F强单调但不需要Lipschitz连续的情况下,为算法提供了一个全局误差界.数值结果表明新算法是有效的.     

一类大规模极小问题的分解并行算法

本文建立了一类大规模极小问题的分解并行算法,证明了算法的总体收敛性与二次终止性.     

一类修正Zhang H.C.非单调共轭梯度算法

为有效求解大规模无约束优化问题,本文基于RMFI共轭梯度法,结合Zhang H.C.非单调线搜索步长规则,提出了一类新的共轭梯度算法.在适当的条件下,证明了新算法的全局收敛性.数值算例表明,新算法比Zhang H.C.非单调规则下的标准RMFI方法收敛速度更快,更有效.同时,本文进一步研究了Zhang H.C.非单调线搜索步长规则的一个基于强迫函数的拓展模型,并从理论上证明了基于此拓展模型的新算法的全局收敛性.     

一类新的基于信赖域技术的非单调共轭梯度算法

为有效求解大规模无约束优化问题,本文基于信赖域技术和修正拟牛顿方程,同时结合Zhang H. C.策略和Gu N. Z.策略,设计了一种新的非单调共轭梯度算法,应用信赖域技术保证了算法的稳健性和收敛性,并给出了算法的全局收敛性分析．在适当条件下,证明了该算法具有线性收敛性．数值实验表明新算法能够有效求解病态和大规模问题．与单独结合其中一种非单调策略的算法相比,新算法需要较少的迭代次数和运行时间,利用其得到的函数值与最优值更接近．     

可导集值向量优化的最优性条件

本文研究了集值优化问题的最优性条件.引入了集值映射Clark切导数的概念,利用Clark切导数,给出了集值优化弱有效解的一个最优性必要条件.建立了集值映射伪凸和拟凸的概念,并获得了弱有效解的两个最优性充分条件.     

稳固非扩张映射不动点集处均衡问题的一种不精确次梯度算法（英文）

本文提出了稳固非扩张映射不动点集处均衡问题的一种新算法.该算法要求双函数是连续的,但不一定是单调的.首先,通过事先引入的参数确定一个闭凸集;其次,根据双函数的不精确次梯度在闭凸集上的投影构造中间迭代点;最后,下一个迭代点由当前迭代点和中间迭代点的凸组合在稳固非扩张算子的映射得到.在适当条件下,本文给出了该算法的全局收敛性证明.     

若干稀疏拟Newton法的单调性

迭代法的单调收敛性问题是迭代法理论研究中的一个重要课题,因为单调收敛的迭代法一般总是大范围收敛的,而且它所给出的近似解序列能够较好地保持所求解的物理特性。例如,求问题正解的单调下降收敛的迭代序列总是正的。拟Newton法是当前解非线性方程组及最优化问题的有效方法之一,然而关于这类方法的单调收敛性问题至今还少有人研究。一般拟Newton法的单调收敛性研究存在着一定的困难。本文研究了若干保稀疏的拟Newton法[2]、[3]的单调收敛性问题,证明了在Newton法具有单调性的类似条件下,上述的稀疏拟Newton法也具有单调性。虽然离散Newton法(见[1])的单调性已有结论,但我们将该算法中迭代的Jacobi近似阵视为由同步全换列过程形成的,而很容易证明它是单调收敛的。     

时标上脉冲动力方程周期边值问题的拟线性化方法

本文研究了一类时标上脉冲动力方程周期边值问题解的收敛性问题.利用时标上一阶脉冲动力不等式、上下解和单调迭代技巧证明了该问题解的一致收敛性结果,并进一步采用拟线性化方法和分析技巧获得了该方程在周期边值条件下两个逼近解序列高阶收敛的充分性判据.本文所得结果发展了时标上动力方程定性理论的结果.     

解非线性方程的三个Steffensen型双侧逼近迭代算法

本文讨论了三类具有不同单调性质单向广义均差的非线性方程,在一定初值条件下极大、极小解的存在性,以及相应的Steffensen型双侧逼近迭代算法的收敛性,并给出了若干数值例子。     

基于稀疏对角拟牛顿方向的非单调超记忆梯度算法

超记忆梯度算法由于其迭代简单和较小的存储需求,在求解大规模无约束优化问题中起着特殊的作用.本文基于稀疏对角拟牛顿技术,结合修正Gu和Mo非单调线搜索步长规则,建立了求解大规模无约束最优化问题的非单调超记忆梯度新算法,给出了算法的全局收敛性分析.新算法具有算法稳定、计算简单的特点可用于求解病态和大规模问题.数值例子表明算法有效稳定.     

An analysis of monotonicity conditions in the mixed hybrid finite element method on unstructured triangulations

In this paper we consider the mixed hybrid finite element method on unstructured triangular grids and evaluate its monotonicity properties by using a non standard set of basis functions for the velocity approximation space. The mixed hybrid discretization of the steady‐state diffusion equation produces a system matrix that depends only on the inner product of the outward normals to the edges of the triangulation and not on the choice of the velocity space basis. This property is used to study the characteristics of the system matrix. It is well known that this matrix is of type M if the angles of the triangulation are not bigger than π/2. An M‐matrix has a nonnegative inverse, i.e. all the elements are nonnegative. This implies the existence of a discrete maximum principle and thus monotonicity of the discretization. We show that, when the triangulation is of Delaunay type and satisfies the property that no circumcenters of boundary elements with Dirichlet conditions lie outside the domain, the inverse of the final matrix is always positive, even in the presence of obtuse angles. Copyright © 2008 John Wiley & Sons, Ltd.     

A variational inequality model of the spatial price network problem with uncertain data

We consider the multicriteria spatial price network equilibrium model in which consumers are allowed to weight both the transportation cost and the transportation time associated with the shipment of a given commodity. In particular, we assume that weights are not deterministic but subject to random fluctuations. Therefore, we formulate the problem as a random variational inequality and prove that under natural assumptions the associated random operator satisfies a uniform monotonicity property. The subsequent analysis is carried out in the framework of the theory of random variational inequalities.     

Fast Methods for Quantitative Eddy-Current Tomography of Conductive Materials

In this paper, we address the imaging of the spatial distribution of the resistivity of conductive materials by using data from eddy-current nondestructive testing. Specifically, the data consists of measurements of the impedance matrix at several frequencies acquired using a coil array. The imaging method processes the second-order term (estimated from the measured data) of the power series expansion, with respect to frequency, of the impedance matrix. This term accounts for the resistive contribution to changes of the impedance matrix, due to the presence of anomalies in the conductor under test, occurring at relatively low frequencies. The operator mapping a given resistivity distribution inside the conductor into the second-order term satisfies a proper monotonicity property. The monotonicity makes it possible to apply a fast noniterative imaging method initially developed by the authors for elliptic problems such as electrical resistance tomography. Numerical examples show the main features of the proposed method, and demonstrate the possibility of real-time imaging.     

Scheduling Production on One Machine with Changeover Costs

A single machine is used to produce several products so as to satisfy known demands over a fixed number of periods. Each time switches are made between products, there are changeover costs as described by a matrix C=[c_ij], where c_ij is the cost of switching from product i to product j. The problem is to find a schedule of production that minimizes the total changeover penalty while meeting the due dates of all customer orders. The function used in a forward-time dynamic program is shown to have a monotonicity property that can be used to advantage when seeking an optimal solution to the problem. This monotonicity property is applied in developing an efficient backward-time search procedure for solving the problem.     

Closed-loop, multiobjective optimization of two-dimensional gas chromatography/mass spectrometry for serum metabolomics

Metabolomics seeks to measure potentially all the metabolites in a biological sample, and consequently, we need to develop and optimize methods to increase significantly the number of metabolites we can detect. We extended the closed-loop (iterative, automated) optimization system that we had previously developed for one-dimensional GC-TOF-MS (O'Hagan, S.; Dunn, W. B.; Brown, M.; Knowles, J. D.; Kell, D. B. Anal. Chem. 2005, 77, 290-303) to comprehensive two-dimensional (GCxGC) chromatography. The heuristic approach used was a multiobjective version of the efficient global optimization algorithm. In just 300 automated runs, we improved the number of metabolites observable relative to those in 1D GC by some 3-fold. The optimized conditions allowed for the detection of over 4000 raw peaks, of which some 1800 were considered to be real metabolite peaks and not impurities or peaks with a signal/noise ratio of less than 5. A variety of computational methods served to explain the basis for the improvement. This closed-loop optimization strategy is a generic and powerful approach for the optimization of any analytical instrumentation.     

非线性指标-3微分-代数系统的波形松弛算法的实现

本文探讨非线性指标-3微分-代数系统的波形松弛算法所涉及的理论模型和具体算例的求解。对于收敛性问题,我们利用谱半径条件证明该理论模型的收敛性,所得结论的收敛性条件相对较弱,并利用算例测试了收敛定理的正确性。结果显示:在求解非线性微分-代数系统时,波形松弛类算法是具有内在并行性的有效算法。     

Decision monotonicity in incremental design: A case study of design for manufacture

Design has often been described as searching the space of solutions to a given problem for either a feasible or optimal solution. Usually, this search is conducted in an incremental, iterative manner. Unfortunately, there is a tendency for the feasible space in some domains to exhibit such poor structure that the incremental design process becomes both difficult and time consuming. This is especially true in the domain of design-for-manufacture by machining. In this paper we present the view that in such cases the sources of ill-structure must be aggressively eliminated by making strategic improvements and modifications to the target technology. To illustrate this point, we show that the domain of design-for-manufacture is ill-structured due to a class of interactions known as global interactions. We then show how global interactions can be virtually eliminated by a combination of a new workholding technology and a new interfacing technique. In the absence of global interactions, we show how the design structure exhibits a property of monotonicity. We describe the ramifications of this monotonicity on the design process, and show how design can then be considered to be deterministic. As a backdrop, we draw examples from other fields where similar strategies have resulted in greater designability.     

Developing a fuzzy proportional–derivative controller optimization engine for engineering design optimization problems

In real world engineering design problems, decisions for design modifications are often based on engineering heuristics and knowledge. However, when solving an engineering design optimization problem using a numerical optimization algorithm, the engineering problem is basically viewed as purely mathematical. Design modifications in the iterative optimization process rely on numerical information. Engineering heuristics and knowledge are not utilized at all. In this article, the optimization process is analogous to a closed-loop control system, and a fuzzy proportional–derivative (PD) controller optimization engine is developed for engineering design optimization problems with monotonicity and implicit constraints. Monotonicity between design variables and the objective and constraint functions prevails in engineering design optimization problems. In this research, monotonicity of the design variables and activities of the constraints determined by the theory of monotonicity analysis are modelled in the fuzzy PD controller optimization engine using generic fuzzy rules. The designer only needs to define the initial values and move limits of the design variables to determine the parameters in the fuzzy PD controller optimization engine. In the optimization process using the fuzzy PD controller optimization engine, the function value of each constraint is evaluated once in each iteration. No sensitivity information is required. The fuzzy PD controller optimization engine appears to be robust in the various design examples tested.     

An augmented EM algorithm for monotonic Bayesian networks using parameterized conditional probability tables

Bayesian networks offer an attractive framework for describing the relationship between latent proficiency variables and observable outcomes. In educational applications, it is useful to restrict the conditional probability tables of the Bayesian network to be monotonic—increasing skill implies a high chance of a good performance. This paper describes the DiBello family of models for Bayesian networks, which enforce monotonicity, and introduces an augmented EM algorithm for estimating the parameters of these models. In a calibration experiment using simulated data, the algorithm did a good job recovering the model parameters and the conditional probability tables with sample sizes as low as 400.

     

A CONTRIBUTION TO THE OPTIMAL DESIGN OF RIDE-RINGS FOR INDUSTRIAL ROTARY KILNS

The design of the ride-rings, or tyres, of industrial rotary kilns is studied as a nonlinear programming problem. The method of monotonicity analysis is employed to obtain results of sufficient generality and utility to the designer. A special-purpose algorithm for the location of the global optimum is presented. A parametric study provides design charts showing the range of criticallity for the various design requirements.

The article represents the type of modeling analysis and subsequent solution, suitable for design problems which must be solved many times with parameter changes larger than those handled with the usual sensitivity analysis.