A lagrangean relaxation algorithm for the constrained matrix problem

We present variants of a convergent Lagrangean relaxation algorithm for minimizing a strictly convex separable quadratic function over a transportation polytope. The algorithm alternately solves two “subproblems,” each of which has an objective function that is defined by using Lagrange multipliers derived from the other. Motivated by the natural separation of the subproblems into independent and very easily solved “subsubproblems,” the algorithm can be interpreted as the cyclic coordinate ascent method applied to the dual problem. We exhibit our computational results for different implementations of the algorithm applied to a set of large constrained matrix problems.     

超精密铣削的三维微加工工艺

本研究旨在对用于获取有雕刻表面金属工件的超精密微加工工艺进行探讨。研究中使用的是车床型的超精密铣床,由分辨率为1nm的X和Z向运动工作台及分辨率为0.0001度的可定位的C轴组成。作为一种铣削工具,一种改进型的由一颗水晶钻构成的“仿球尖铣刀”被放置在X轴的高速气浮轴承之上。这样一来,X轴和C轴的协调运动就可产生三维铣削的效果。为提高表面粗糙度,通过模拟我们研究的刀具边沿和工件表面的接触情况,结果发现,刀具低速进给时切削比较有效。作为三维微加工工艺的一个例子,运用数字仪提供的扫描数据在一个直径为3mm的铜表面上制作一个传统的NOH面罩。经证明,超精密铣床有潜力加工出表面粗糙度为69nm(P—V值)的工件。     

The traveling salesman problem: An update of research

During the course of the last few years, attacks on the traveling salesman problem have resulted in a variety of often innovative and rather powerful computational procedures. In this article, we present a review of these results for problems defined on weighted and unweighted graphs. Some account of computational behavior for exact algorithms is provided; however, the primary coverage deals with the strategy of particular procedures. In addition, we include some aspects of nonexact algorithms with major interest confined to the establishment of worst-case bounds.     

A game theoretic approach to a two firm bidding problem

In this paper a model is developed for determining optimal strategies for two competing firms which are about to submit sealed tender bids on K contracts. A contract calls for the winning firm to supply a specific amount of a commodity at the bid price. By the same token, the production of that commodity involves various amounts of N different resources which each firm possesses in limited quantities. It is assumed that the same two firms bid on each contract and that each wants to determine a bidding strategy which will maximize its profits subject to the constraint that the firm must be able to produce the amount of products required to meet the contracts it wins. This bidding model is formulated as a sequence of bimatrix games coupled together by N resource constraints. Since the firms' strategy spaces are intertwined, the usual quadratic programming methods cannot be used to determine equilibrium strategies. In lieu of this a number of theorems are given which partially characterize such strategies. For the single resource problem techniques are developed for determining equilibrium strategies. In the multiple resource problem similar methods yield subequilibrium strategies or strategies that are equilibrium from at least one firm's point of view.