8th International Conference on Operational Research KOI 2000
Rovinj, Croatia, September 27 - 29, 2000
Optimality and Stability in Operations Research: Short Stories
Sanjo Zlobec
Department of Mathematics and Statistics, McGill University, (Montreal QC, Canada)
Abstract
This talk briefly reviews the development of the two basic notions in
operations research from its early history to the current state. This is done selectively,
and often informally. Some of the following topics will be discussed:
In the beginning...
400000 Chinese chasing a dream (reported in Kuangming Daily, Nov. 1, 1969)
One optimum in LP better than another ?
Puzzled Russians
An LP model unstable ? Give me a break !
Identifying instability in LP
Optimality meets stability...
Optimal parameters in LP and convex models
Optimality without stability is not the same...
Something recent and abstract (Or: When “parameters” becomes “controls”...)
Details can be found in the papers by the speaker, such as:
- "Parametric programming: An illustrative mini-encyclopedia", Mathematical Communications 5(2000) 1-39.
- "Stability in linear programming models: An index set approach", Annals of Operations Research (2000, forthcoming). Preprint available upon request.
- "Nondifferentiable optimization: Parametric programming", in (Floudas, C.A. and P.M. Pardalos, eds.): Encyclopedia of Optimization, Kluwer Academic (2000, forthcoming)
- "Convex parametric programming in abstract spaces", (jointly with M. Asgharian) submitted to Optimization. Preprint available upon request.
- "The Fritz John condition", Encyclopedia of Mathematics; Supplement 3, Kluwer Academic (2001, forthcoming)
- Stable Parametric Programming, forthcoming book