Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more.


Table of Contents Multivariate Data Optimization Introduction
See also: phase space, response function, Simplex Algorithm 

Optimization
Introduction

Optimization problems are arising in nearly all fields of science and technology. Therefore the range of problems is huge and a large number of possible approaches for solutions are available. Here are some examples of optimization problems:
 

    A company producing electronic devices needs to optimize the quality assurance procedure: more elaborate testing increases the overall production costs, while an excessive amount of low quality products will result in complaints and a degradation in the image of the company.

    A mathematician has to optimize the bus schedule of a city. The timing of the buses has to be optimized considering several constraints: a minimum number of buses per hour; optimum alignment of the departure times to the higher order railway and subway system; unusual traffic densities at certain locations which may slow down the buses; ....

    An analytical chemist has to set up a mass spectrometer for high resolution measurements. One of the prerequisites is that the voltages at the deflection lenses of the ion accelerator have to be set in a way that the ion beam shows a rectangular cross-section with uniform ion density.
     

These examples give a quick impression of the diversity of optimization problems. In more general terms, the optimization process can be defined as finding the minimum (or the maximum) of a response function f (sometimes called an objective function or quality function). The response function may be rather complicated and of high dimensionality. From a computational standpoint, any optimizing has to be done quickly and cheaply, which usually means that the response function f should be evaluated as few times as possible during the optimization process.
 

Last Update: 2006-Jan-17