Convergence of splitting and Newton methods for complementarity problems: An application of some sensitivity results

This paper is concerned with two well-known families of iterative methods for solving the linear and nonlinear complementarity problems. For the linear complementarity problem, we consider the class of matrix splitting methods and establish, under a finiteness assumption on the number of solutions, a necessary and sufficient condition for the convergence of the sequence of iterates produced. A rate of convergence result for this class of methods is also derived under a stability assumption on the limit solution. For the nonlinear complementarity problem, we establish the convergence of the Newton method under the assumption of a pseudo-regular solution which generalizes Robinson's concept of a strongly regular solution. In both instances, the convergence proofs rely on a common sensitivity result of the linear complementarity problem under perturbation.This work was based on research supported by the National Science Foundation under grant ECS-8717968.     

On the convergence of the exponential multiplier method for convex programming

In this paper, we analyze the exponential method of multipliers for convex constrained minimization problems, which operates like the usual Augmented Lagrangian method, except that it uses an exponential penalty function in place of the usual quadratic. We also analyze a dual counterpart, the entropy minimization algorithm, which operates like the proximal minimization algorithm, except that it uses a logarithmic/entropy proximal term in place of a quadratic. We strengthen substantially the available convergence results for these methods, and we derive the convergence rate of these methods when applied to linear programs.Research supported by the National Science Foundation under Grant DDM-8903385, and the Army Research Office under Grant DAAL03-86-K-0171.     

On the global optimization properties of finite-difference local descent algorithms

The paper is devoted to the convergence properties of finite-difference local descent algorithms in global optimization problems with a special -convex structure. It is assumed that the objective function can be closely approximated by some smooth convex function. Stability properties of the perturbed gradient descent and coordinate descent methods are investigated. Basing on this results some global optimization properties of finite-difference local descent algorithms, in particular, coordinate descent method, are discovered. These properties are not inherent in methods using exact gradients.The paper was presented at the II. IIASA-Workshop on Global Optimization, Sopron (Hungary), December 9–14, 1990.     

C 1 surface interpolation with constraints

Givenn pairwise distinct and arbitrarily spaced pointsP _i in a domainD of thex–y plane andn real numbersf _i, consider the problem of computing a bivariate functionf(x, y) of classC ¹ inD whose values inP _i are exactlyf _i,i=1,,n, and whose first or second order partial derivatives satisfy appropriate equality and inequality constraints on a given set ofp pointsQ _l inD.In this paper we present a method for solving the above problem, which is designed for extremely large data sets. A step of this method requires the solution of a large scale quadratic programming (QP) problem.The main purpose of this work is to analyse an iterative method for determining the solution of this QP problem: such a method is very efficient and well suited for parallel implementation on a multiprocessor system.Work supported by MURST Project of Computational Mathematics, Italy.     

Random walk on distant mesh points Monte Carlo methods

A new technique for obtaining Monte Carlo algorithms based on the Markov chains with a finite number of states is suggested. Instead of the classical random walk on neighboring mesh points, a general way of constructing Monte Carlo algorithms that could be called random walk on distant mesh points is considered. It is applied to solve boundary value problems. The numerical examples indicate that the new methods are less laborious and therefore more efficient.In conclusion, we mention that all Monte Carlo algorithms are parallel and could be easily realized on parallel computers.     

SYNTHESIS OF SODALITE BY DRY POWDER METHOD

用新颖的干粉方法合成系列沸石的研究已从五元环沸石延伸到具有四元环和六元环的方钠石。本研究运用干粉方法在Ｎａ２Ｏ－ＳｉＯ２－Ａｌ２Ｏ３混合物中分别以乙醇胺和乙二胺－氟化物为模板，合成出了方钠石。有机模板剂以吸附态模板方式进入体系。用ＸＲＤ数据、扫描电镜图及红外光谱测试结果对实验产品做了表征。结果表明，干粉体系制备的方钠石的晶胞参数小于水热体系和非水体系合成的方钠石的相应值。而以乙醇胺为模板制备的方钠石与以乙二胺－氟化物为模板的样品比较，后者具有较快的晶化速度、较小的晶胞体积和晶粒     

Thermodynamics of electrolyte solutions. The system HCl + CaCl2 + H2O at 298.15°K

Activity coefficients of hydrochloric acid have been determined from electromotive-force measurements of cells containing mixtures of hydrochloric acid and calcium chloride at constant total ionic strengthsI=0.1, 0.5, 1.0, 2.0, and 3.0 mole-kg^–1 at 298.15°K. Interpretations based on Scatchard's and Pitzer's equations indicate that Pitzer's equations probably provide a more convenient guide to the thermodynamic properties of the mixed-electrolyte solutions. Activity coefficients for calcium chloride were derived from these equations.     

Evolution of the structural stability of large Cu,Ni, Pd,and Ag clusters with size: An analysis within the embedded atom method

A study of the structural stability of clusters made up of a single component has been carried out within the Embedded Atom Method. Perfect icosahedral and cuboctahedral Cu, Ni, Pd, and Ag clusters with up to 5083 atoms have been compared. The icosahedron is found to be the stable structure for small clusters, and a change of structure from icosahedral to cuboctahedral is found as the cluster size increases. A contraction of the interatomic distances results when the cluster size decreases.     

碱金属和重金属叠氮化物的感度和导电性研究

分别用EHCO和DV－X_α方法，计算研究了α－NaN_3、β-NaN_3和AgN_3的能带结构和原子簇电子结构. AgN_3与NaN_3相比：带隙(△Eg)较小、带宽(BW)较大，因而电导率较大. 比较前沿晶体轨道(CO)和前沿分子轨道(MO)的能级、组成及电子在其间的跃迁；预示AgN_3比NaN_3更敏感、更易分解和起爆．还从电子微观层次揭示了金属叠氮化物的导电性和爆炸性之间的联系．     

离子缔合富集明极溶出伏安法测定痕量碘——Ⅰ.以丁基罗丹明B为离子缔合剂

本文提出在0.1mol/LH_2SO_4,7.5×10~(-4)mol/LBr~-和6×10~(-5)mol/L丁基罗丹明B(R~+)的底液中,在+1.0V下,I~-离子于玻璃电极上被氧化生成I_2BrR离子缔合物,藉以阴极溶出伏安法测定碘、I~-离子浓度在1～50ppb范围内与峰电流呈线性关系。用于食盐中痕碘的测定。