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Scenario optimization
The scenario approach or scenario optimization approach is a technique for obtaining solutions to robust optimization and chance-constrained optimization problems based on randomization of the constraints. The technique has existed for decades as a heuristic approach and has more recently been given a systematic theoretical foundation.
== Description ==
In optimization, robustness features translate into constraints that are parameterized in the uncertain elements of the problem. The scenario method〔G. Calafiore and M.C. Campi. ''Uncertain Convex Programs: Randomized Solutions and Confidence Levels.'' Mathematical Programming, 102: 25–46, 2005. ()〕〔G. Calafiore and M.C. Campi. "The scenario approach to robust control design," IEEE Transactions on Automatic Control, 51(5). 742-753, 2006. ()〕〔M.C. Campi and S. Garatti. ''The Exact Feasibility of Randomized Solutions of Uncertain Convex Programs.'' SIAM J. on Optimization, 19, no.3: 1211–1230, 2008.()〕 simply consists in extracting at random some instances of the uncertainty, and then finding the optimal solution of a problem where only the constraints associated to the extracted uncertainty instances are considered. The theory tells the user how “robust” this solution is, that is whether and to what extent the found solution satisfies the constraints occurring for other unseen instances of the uncertainty. Thus, this theory justifies at a solid theoretical level the use of randomization in robust and chance-constrained optimization.
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