关于求线性规划初始可行基的生成算法

本文用反例证明了文「１」提出的求线性规划寝可行基的生成算法有错误,并给出了修正的生成算法。     

Hilbert空间中求解分裂可行问题CQ算法的强收敛性

在Hilbert空间中,为了研究分裂可行问题迭代算法的强收敛性,提出了一种新的CQ算法.首先利用CQ算法构造了一个改进的Halpern迭代序列； 然后通过把分裂可行问题转化为算子不动点， 在较弱的条件下， 证明了该序列强收敛到分裂可行问题的一个解. 推广了Wang和Xu的有关结果.     

单调变分不等式可行与非可行点组合的连续算法

本文给出了单调变分不等式问题一个新的连续型求解方法，方法的实现依赖于一系列含有四个参数的摄动单调变分不等式的求解．其中摄动参数要求的条件较为温和，这使得本文方法成为可行点与非可行点算法的有机组合和统一．在适当的假设条件下，我们分析和证明了摄动变分不等式问题解的存在性，唯一性和算法的强收敛性．     

线性规划的基解算法

提出了求解线性规划问题的一种新方法-基解算法,它是一个不需引入人工变量,不必预先求出一个可行基的直接求解算法。     

求解凸二次规划问题的不可行内点算法

该文对一般的凸二次规划问题，给出了一个不可行内点算法，并证明了该算法经过犗（狀２犔）步迭代之后，要么得到问题的一个近似最优解，要么说明该问题在某个较大的区域内无解．     

一种原始——对偶单纯形算法的枢轴准则选择

Curet曾提出了一种有趣的原始一对偶技术,在优化对偶问题的同时单调减少原始不可行约束的数量,当原始可行性产生时也就产生了原问题的最优解.然而该算法需要一个初始对偶可行解来启动,目标行的选择也是灵活、不确定的.根据Curet的原始一对偶算法原理,提出了两种目标行选择准则,并通过数值试验进行比较和选择.对不存在初始对偶可行解的情形,通过适当改变目标函数的系数来构造一个对偶可行解,以求得一个原始可行解,再应用原始单纯形算法求得原问题的最优解.数值试验对这种算法的计算性能进行验证,通过与经典两阶段单纯形算法比较,结果表明,提出的算法在大部分问题上具有更高的计算效率.     

非线性最优化一个超线收敛的可行下降算法

本文讨论非线性等式和不等式约束最优化的求解方法。首先将原问题扩充成一个只含不等式约束的参数规划，对于充分大的参数，扩充问题与原问题是等价的。然手建立具有以下特点的一个新算法。１）算法对扩充问题而言是可行下降的，参数只须自动调整有限次；２）每次迭代仅需解一个二次规划；３）在适当的假设下，算法超线性收敛于原问题的最优解。     

单纯形法的旋转迭代算法及影子价格

本文对线性规划问题提出一种寻找初始可行基和判定可行解的统一方法，它在运用单纯形法时，在若干情况下不必引入人工变量而可在一种表格之下直接应用旋转运算而获得，之后就在同一张表格下完全和常规单纯形法一样求最优解，此法我们称之为“单纯形法的旋转迭代算法”，应用此法，我们容易求出影子价格。     

分裂可行问题的1-范数正则化方法

主要研究了分裂可行问题的1-范数正则化.首先利用1-范数正则化方法,将分裂可行问题转化为无约束优化问题.其次讨论了1-范数正则化解的若干性质,并给出了求解1-范数正则化解的邻近梯度算法.最后通过数值试验验证了算法的可行性和有效性.     

物流中心选址模型及一种启发式算法

本建立了特流系统分析中的一个物流中心选址模型，它属非线性混合0－1规划。为克服求解上的困难，首先利用其特殊结构，建立了一个分解－过滤模式，进而对导出的可行子问题给出了一种实用的启发式算法。     

A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package

The application of multi-attribute utility theory whose aggregation process is based on the Choquet integral requires the prior identification of a capacity. The main approaches to capacity identification proposed in the literature are reviewed and their advantages and inconveniences are discussed. All the reviewed methods have been implemented within the Kappalab R package. Their application is illustrated on a detailed example.     

Nonparametric criteria for supervised classification of fuzzy data

The supervised classification of fuzzy data obtained from a random experiment is discussed. The data generation process is modelled through random fuzzy sets which, from a formal point of view, can be identified with certain function-valued random elements. First, one of the most versatile discriminant approaches in the context of functional data analysis is adapted to the specific case of interest. In this way, discriminant analysis based on nonparametric kernel density estimation is discussed. In general, this criterion is shown not to be optimal and to require large sample sizes. To avoid such inconveniences, a simpler approach which eludes the density estimation by considering conditional probabilities on certain balls is introduced. The approaches are applied to two experiments; one concerning fuzzy perceptions and linguistic labels and another one concerning flood analysis. The methods are tested against linear discriminant analysis and random K-fold cross validation.     

An improvement over the GVW algorithm for inhomogeneous polynomial systems

The GVW algorithm provides a new framework for computing Gröbner bases efficiently. If the input system is not homogeneous, some J-pairs with larger signatures but lower degrees may be rejected by GVW's criteria, and instead, GVW has to compute some J-pairs with smaller signatures but higher degrees. Consequently, degrees of polynomials appearing during the computations may unnecessarily grow up higher, and hence, the total computations become more expensive. This phenomenon happens more frequently when the coefficient field is a finite field and the field polynomials are involved in the computations. In this paper, a variant of the GVW algorithm, called M-GVW, is proposed. The concept of mutant pairs is introduced to overcome the inconveniences brought by inhomogeneous inputs. In aspects of implementations, to obtain efficient implementations of GVW/M-GVW over boolean polynomial rings, we take advantages of the famous library M4RI. We propose a new rotating swap method of adapting efficient routines in M4RI to deal with the one-direction reductions in GVW/M-GVW. Our implementations are tested with many examples from Boolean polynomial rings, and the timings show M-GVW usually performs much better than the original GVW algorithm if mutant pairs are found.     

Planning wireless networks by shortest path

Transmitters and receivers are the basic elements of wireless networks and are characterized by a number of radio-electrical parameters. The generic planning problem consists of establishing suitable values for these parameters so as to optimize some network performance indicator. The version here addressed, namely the Power Assignment Problem (pap), is the problem of assigning transmission powers to the transmitters of a wireless network so as to maximize the satisfied demand. This problem has relevant practical applications both in radio-broadcasting and in mobile telephony. Typical solution approaches make use of mixed integer linear programs with huge coefficients in the constraint matrix yielding numerical inaccuracy and poor bounds, and so cannot be exploited to solve large instances of practical interest. In order to overcome these inconveniences, we developed a two-phase heuristic to solve large instances of pap, namely a constructive heuristic followed by an improving local search. Both phases are based on successive shortest path computations on suitable directed graphs. Computational tests on a number of instances arising in the design of the national Italian Digital Video Broadcasting (DVB) network are presented.     

Aerodynamic effects caused by a train entering a tunnel

The entrance of a train head in a tunnel causes a pressure wave with a steep gradient followed by a further, but less steep increase of the pressure due to friction on the train and tunnel wall, respectively, caused by the entrance of the train body (Fig. 1). This pressure increase is terminated by the entrance of the tail of the train causing a rarefaction wave, if the tunnel is long enough, so that there are no in.uences of reflected waves from the opposite tunnel portal. Since pressure transients in a railway tunnel may cause inconveniences to passengers and tunnel workers, respectively, it is important to have a reliable method for calculating the pressure history of a train passing a tunnel. Results from full‐scale experiments show only minor variations of the pressure over the cross‐section of the tunnel, if the measuring point is not too close to the entrance portal. Therefore CFD‐programs for viscid flow onedimensional in space give rather reliable results. Such programs are applicable for the whole passage of one or more trains through a tunnel at the same time [1]. The pressure history of a passage of a train through a tunnel is dominated by the propagation and reflection of the wave of the first pressure increase due to head and body entrance. It is important to estimate these effects as simple as possible and to show the influences of the main parameters like Mach number and blockage ratio. A rather simple formula is given for the first two pressure peaks and the results are compared to results from CFD‐calculations.     

Approximation of a nonlinear degenerate parabolic equation via a linear relaxation scheme

We study a nonlinear degenerate parabolic equation of the type accompanied by an initial datum and mixed boundary conditions. The symbol [ · ]₊ denotes the usual cutoff function. The problem represents a model of a reactive solute transport in porous media. The exponent p fulfills p ∈ (0, 1). This limits the regularity of a solution and leads to inconveniences in the error analysis. We design a new robust linear numerical scheme for the time discretization. This is based on a suitable combination of the backward Euler method and a linear relaxation scheme. We prove the convergence of relaxation iterations on each time point t_i. We derive the error estimates in suitable function spaces for all values of p ∈ (0, 1). © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005.     

Graphical Diagnostics for Markov Models for Categorical Data

Markov models are widely used as a method for describing categorical data that exhibit stationary and nonstationary autocorrelation. However, diagnostic methods are a largely overlooked topic for Markov models. We introduce two types of residuals for this purpose: one for assessing the length of runs between state changes, and the other for assessing the frequency with which the process moves from any given state to the other states. Methods for calculating the sampling distribution of both types of residuals are presented, enabling objective interpretation through graphical summaries. The graphical summaries are formed using a modification of the probability integral transformation that is applicable for discrete data. Residuals from simulated datasets are presented to demonstrate when the model is, and is not, adequate for the data. The two types of residuals are used to highlight inadequacies of a model posed for real data on seabed fauna from the marine environment.

Supplemental materials, including an R-package RMC with functions to perform the diagnostic measures on the class of models considered in this article, are at the journal’s website. The R-package is also available at CRAN.     

Monotonicity criteria for difference schemes designed for hyperbolic equations

Previously formulated monotonicity criteria for explicit two-level difference schemes designed for hyperbolic equations (S.K. Godunov’s, A. Harten’s (TVD schemes), characteristic criteria) are extended to multileveled, including implicit, stencils. The characteristic monotonicity criterion is used to develop a universal algorithm for constructing high-order accurate nonlinear monotone schemes (for an arbitrary form of the desired solution) based on their analysis in the space of grid functions. Several new fourth-to-third-order accurate monotone difference schemes on a compact three-level stencil and nonexpanding (three-point) stencils are proposed for an extended system, which ensures their monotonicity for both the desired function and its derivatives. The difference schemes are tested using the characteristic monotonicity criterion and are extended to systems of hyperbolic equations.     

Multilevel Preconditioners for Mixed Methods for Second Order Elliptic Problems

A new approach for constructing algebraic multilevel preconditioners for mixed finite element methods for second order elliptic problems with tensor coefficients on general geometry is proposed. The linear system arising from the mixed methods is first algebraically condensed to a symmetric, positive definite system for Lagrange multipliers, which corresponds to a linear system generated by standard nonconforming finite element methods. Algebraic multilevel preconditioners for this system are then constructed based on a triangulation of the domain into tetrahedral substructures. Explicit estimates of condition numbers and simple computational schemes are established for the constructed preconditioners. Finally, numerical results for the mixed finite element methods are presented to illustrate the present theory.