Classical robust optimization

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Author Names: Andre Ramirez-Cedeno
Steward: Fengqi You, Dajun Yue

Contents

Classical Robust Optimization

Indroduction and History

Robust optimization is a subset of optimization theory that deals with a certain measure of robustness vs uncertainty. This balance of robustness and uncertainty is represented as variability in the parameters of the problem at hand and or its solution. Robust optimization dates back to the beginning of modern decision theory in the 1950’s. It became a discipline of its own in the 1970’s with paralleled development in other technological fields. Robust optimization has many applications in statistics, chemical engineering, finance, pharmaceuticals and computer science. In engineering, this theory often is referred to as “Robust Design Optimization’ of “Reliability Based Design”.

What is Robustness?

Robustness refers to the ability of a system to cope with errors during an execution. It can also be defined as the ability of an algorithm to continue operating despite abnormalities in calculations. Most algorithms try to find a balance between robustness and efficiency/execution time.

Simple Mathematical Example

 Max 5X + 2Y

      s.t. cX + dY <= 15
           X >= 0
           Y >= 0
           For All c,d \in P