Necessary and Sufficient Conditions of Unacceptable Solutions in LP Discriminant Analysis*

Characterization of unacceptable solutions for linear programming (LP) discriminant models have been discussed in the literature and the results presented so far are not satisfactory. This paper establishes necessary and sufficient conditions of unacceptable solutions for a number of LP models, addresses the practical implications of these conditions, and discusses the relationship between unacceptable solutions and multiple solutions.     

等厚干涉条纹的数据处理

讨论等厚干涉条纹的数据处理方法，对一元线性回归和非线性优化方法进行比较，得到非一性优化方法明显优于一元线性回归的结论，非线性优化方法对干涉条纹数较少的情况尤为适用。     

线性规划最优解的探讨及在生产与运作管理中的应用

本文研究了线性规划问题的最优解并将其应用于生产与运作管理问题 ,提出了三种最优解的判别准则     

Sensitivity of Linear Programs to Related Changes in Multiple Inputs*

In a 1991 paper in Decision Sciences, Camm and Burwell presented smart modeling techniques for obtaining the sensitivity of linear programs to simultaneous common changes in common inputs. This note addresses sensitivity analysis of simultaneous related changes in multiple inputs, and shows how related multi-parametric analysis can be performed with software that has no or only limited parametric programming capability.     

Analyzing and Modeling the Maximum Diversity Problem by Zero-One Programming*

The problem of maximizing diversity deals with selecting a set of elements from some larger collection such that the selected elements exhibit the greatest variety of characteristics. A new model is proposed in which the concept of diversity is quantifiable and measurable. A quadratic zero-one model is formulated for diversity maximization. Based upon the formulation, it is shown that the maximum diversity problem is NP-hard. Two equivalent linear integer programs are then presented that offer progressively greater computational efficiency. Another formulation is also introduced which involves a different diversity objective. An example is given to illustrate how additional considerations can be incorporated into the maximum diversity model.     

Minimizing Misclassifications in Linear Discriminant Analysis*

A procedure is developed for determining two-group linear discriminant classifiers that misclassify the fewest number of observations in the training sample. An experimental study confirms the value of this approach.     

Note on Second-Order Polynomial Regression Models

Polynomial regression models have applications in the social sciences and in business research. Unfortunately, such models have a high degree of multicollinearity that creates problems with the statistical assessment of the model. In fact, the collinearity may be so severe that it could lead to an incorrect conclusion that some of the terms in the model are not statistically significant and should therefore be omitted from the model. This note provides a simple transformation to achieve orthogonality in polynomial models between the linear and quadratic terms, thereby eliminating the collinearity problem. It also shows that the same procedure does not achieve orthogonality for higher-order terms. An example data set is analyzed to show the benefits of such a procedure.     

Stock Evaluation Using a Preference Disaggregation Methodology

This paper presents a real application of a multicriteria decision aid (MCDA) approach to portfolio selection based on preference disaggregation, using ordinal regression and linear programming (UTADIS method; UTilités Additives DIScriminantes). The additive utility functions that are derived through this approach have the extrapolation ability that any new alternative (share) can be easily evaluated and classified into one of several user-predefined groups. The procedure is illustrated with a case study of 98 stocks from the Athens stock exchange, using 15 criteria. The results are encouraging, indicating that the proposed methodology could be used as a tool for the analysis of the portfolio managers' preferences and choices. Furthermore, the comparison with multiple discriminant analysis (either using a stepwise procedure or not) illustrates the superiority of the proposed methodology over a well-known multivariate statistical technique that has been extensively used to study financial decision-making problems.     

Notes and Communications RESOLVING CERTAIN DIFFICULTIES AND IMPROVING THE CLASSIFICATION POWER OF LP DISCRIMINANT ANALYSIS FORMULATIONS

In certain settings, difficulties arise that limit the effectiveness of LP formulations for the discriminant problem. Explanations and possible remedies have been offered, but these have had only limited success. We provide a simple way to overcome these problems based on an appropriate use and interpretation of normalizations. In addition, we demonstrate a normalization that is invariant under all translations of the problem data, providing a stability property not shared by previous approaches. Finally, we discuss the possibility of using more general models to improve discrimination.