Review article

Parametric programming: An illustrative mini encyclopedia

S. Zlobec

Abstract

Parametric programming is one of the broadest areas of applied mathematics. Practical problems, that can be described by parametric programming, were recorded in the rock art about thirty
millennia ago. As a scientific discipline, parametric programming began emerging only in the 1950's. In this tutorial we introduce, briefly study, and illustrate some of the elementary
notions of parametric programming. This is done using a limited theory (mainly for linear and convex models) and by means of examples, figures, and solved real-life case studies.
Among the topics discussed are stable and unstable models, such as a projectile motion model (maximizing the range of a projectile), bilevel decision making models and von Stackelberg games of market economy, law of refraction and Snell's law for the ray of light, duality,
Zermelo's navigation problems under the water, restructuring in a textile mill, ranking of efficient DMU (university libraries) in DEA, minimal resistance to a gas flow, and semi-abstract parametric programming models. Some numerical methods of input optimization
are mentioned and several open problems are posed.

Keywords

parametric programming; optimal parameter; convex programming; point-to-set mapping; stable model; unstable model; input optimization; optimal control; duality

Hrčak ID:

861

URI

https://hrcak.srce.hr/861

Publication date:

20.6.2000.

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