Random polytopes: Their definition,generation and aggregate properties

The definition of random polytope adopted in this paper restricts consideration to those probability measures satisfying two properties. First, the measure must induce an absolutely continuous distribution over the positions of the bounding hyperplanes of the random polytope; and second, it must result in every point in the space being equally as likely as any other point of lying within the random polytope. An efficient Monte Carlo method for their computer generation is presented together with analytical formulas characterizing their aggregate properties. In particular, it is shown that the expected number of extreme points for such random polytopes increases monotonically in the number of constraints to the limiting case of a polytope topologically equivalent to a hypercube. The implied upper bound of 2 ⁿ wheren is the dimensionality of the space is significantly less than McMullen's attainable bound on the maximal number of vertices even for a moderate number of constraints.     

Nonlinear programming via an exact penalty function: Global analysis

In this paper we motivate and describe an algorithm to solve the nonlinear programming problem. The method is based on an exact penalty function and possesses both global and superlinear convergence properties. We establish the global qualities here (the superlinear nature is proven in [7]). The numerical implementation techniques are briefly discussed and preliminary numerical results are given.This work is supported in part by NSERC Grant No. A8639 and the U.S. Dept. of Energy.     

Polyhedral extensions of some theorems of linear programming

Three theorems of linear programming form our starting point: Tucker's theorem (1956) concerning the existence of optimal solutions satisfying the complementary slackness conditions strictly, and Williams' two theorems (1970) concerning the coordinatewise complementary behavior of feasible and optimal solutions. Here, we establish that the same phenomena hold in another, more versatile framework involving general polyhedral convexity. As one main application, the results are transferred into the context of the monotone complementarity problem. Several other theoretical applications are indicated.Research supported in part by the National Science Foundation under grant number MCS 79-05793 at the University of Illinois at Urbana-Champaign.     

Numerically stable methods for quadratic programming

Numerically stable algorithms for quadratic programming are discussed. A new algorithm is described for indefinite quadratic programming which utilizes methods for updating positivedefinite factorizations only. Consequently all the updating procedures required are common to algorithms for linearly-constrained optimization. The new algorithm can be used for the positive-definite case without loss of efficiency.     

Part-compilation in high-level languages

Many programming languages include the ability to divide large programs into smaller segments, which are compiled separately. When a small modification is made to a large program, then the affected segment only has to be re-compiled.This paper discusses how high-level languages like Algol 68, Algol W or Simula 67 can incorporate part-compilation in a usable, secure and efficient way.     

线性比式和规划问题的输出空间分支定界算法

本文旨在针对线性比式和规划这一NP-Hard非线性规划问题提出新的全局优化算法.首先,通过引入p个辅助变量把原问题等价的转化为一个非线性规划问题,这个非线性规划问题的目标函数是乘积和的形式并给原问题增加了p个新的非线性约束,再通过构造凸凹包络的技巧对等价问题的目标函数和约束条件进行相应的线性放缩,构成等价问题的一个下界线性松弛规划问题,从而提出了一个求解原问题的分支定界算法,并证明了算法的收敛性.最后,通过数值结果比较表明所提出的算法是可行有效的.     

Performance appraisal based on distance function methods

Performance appraisal is a process used by some firms to evaluate their employees’ efficiency and productivity in order to plan their promotion policy, salary policy, layoffs policy, etc. Initially this process was just carried out by the executive staff, but recently it has evolved into an evaluation process based on the opinion of different reviewers, supervisors, collaborators, customers and the employees themselves (360-degree method). In such an evaluation process the reviewers evaluate some indicators related to employees performance appraisal. In this paper we propose an evaluation framework where there are different sets of reviewers taking part in the evaluation process. Since reviewers have a different knowledge about the evaluated employee, it seems suitable to offer a flexible framework in which different reviewers can express their assessments in different finite scales according to their knowledge. The final aim is to compute a global evaluation for each employee, that can be used by the management team to make their decisions regarding their human resources policy. In this way, to obtain a global evaluation for each employee, we propose a methodology able to aggregate individual valuation in a metric L_p framework. In this context, the associated optimization problems can be reduced to an Extended Goal Programming formulation that is very easy to compute.     

A flexible approach to ranking with an application to MBA Programs

We develop a model for flexibly ranking multi-dimensional alternatives/units into preference classes via Mixed Integer Programming. We consider a linear aggregation model, but allow the criterion weights to vary within pre-specified ranges. This allows the individual alternatives/units to play to their strengths. We illustrate the use of the model by considering the Financial Times Global MBA Program rankings and discuss the implications. We argue that in many applications neither the data nor the weights or the aggregation model itself is precise enough to warrant a complete ranking, providing an argument for sorting or what we call flexible ranking.     

Languages for Statistics and Data Analysis

Abstract

Languages for data analysis and statistics must be able to cover the entire spectrum from improvisation and fast prototyping to the implementation of streamlined, specialized systems for routine analyses. Such languages must not only be interactive but also programmable, and the distinctions between language, operating system, and user interface get blurred. The issues are discussed in the context of natural and computer languages, and of the different types of user interfaces (menu, command language, batch). It is argued that while such languages must have a completely general computing language kernel, they will contain surprisingly few items specific to data analysis—the latter items more properly belong to the “literature” (i.e., the programs) written in the language.     

On selecting portfolio of international mutual funds using goal programming with extended factors

This paper proposes and investigates the use of several factors for portfolio selection of international mutual funds. Three of the selected factors are specific to mutual funds, additional three factors are taken from Macroeconomics and one factor represents regional and country preferences. Each factor is treated as an objective in the multiple objective approach of goal programming. Three variants of goal programming are utilized.