An investigation of the use of goal programming to fit response surfaces

Article Abstract:

The use of goal programming (GP) models in applications of response surface methodology is considered. Specifically, the GP-based L1-norm criterion (LGP) is introduced as an alternative to the ordinary least squares (OLS) method. Subsequently, a performance comparison between three LGP methods and the OLS is conducted using Monte Carlo simulation and multivariate ANOVA analysis. The results showed two LGP methods provided a more accurate solution at lesser convergence speed.

Statistics, Graphic methods, Statistics (Mathematics), Least squares, Response surfaces (Statistics)

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Algebraic languages for mathematical programming

Article Abstract:

Algebraic modeling languages for mathematical programming applications are evaluated. An algebraic language is a formal description of objective functions and constraints of an optimization model in an algebraic format. Prominent features of the languages are analyzed to determine their level of applicability to human techniques of model derivation. Features include model and data separation and language interpreter integration to other mathematical programming components.

Evaluation, Mathematical models, Language and languages

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A mathematical programming approach to clusterwise regression model and its extensions

Article Abstract:

A study was conducted to examine the use of the clusterwise regression method to carry out cluster analysis within a regression framework. The estimation of the clusterwise regression was a tough combinatorial optimization problem. A generalized clusterwise regression model was then formulated as a mathematical programming problem. In addition, the cluster membership and discriminant parameters were determined simultaneously using another nonlinear programming technique.

Analysis, Algorithms, Cluster analysis

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