Robust optimization

Robust optimization is a field of optimization theory that deals with optimization problems in which a certain measure of robustness is sought against uncertainty that can be represented as deterministic variability in the value of the parameters of the problem itself and/or its solution.

The origins of robust optimization date back to the establishment of modern decision theory in the 1950s and the use of worst case analysis and Wald's maximin model as a tool for the treatment of severe uncertainty. It became a discipline of its own in the 1970s with parallel developments in several scientific and technological fields. Over the years, it has been applied in statistics, but also in operations research,electrical engineering,control theory,finance,portfolio managementlogistics,manufacturing engineering,chemical engineering,medicine, and computer science. In engineering problems, these formulations often take the name of "Robust Design Optimization", RDO or "Reliability Based Design Optimization", RBDO.

Consider the following linear programming problem

where ${\displaystyle P}$ is a given subset of ${\displaystyle \mathbb {R} ^{2}}$.

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