Introduction to the Scenario Approach

The scenario approach addresses uncertain convex optimization problems. This includes robust linear and quadratic programs, and the optimization problems with parameter-dependent linear matrix inequalities (LMIs). By appropriate sampling of the constraints, one obtains a convex optimization problem (the scenario problem) that can be solved by means of standard optimization solvers. The so-obtained solution bears precise probabilistic guarantees of robustness. The scenario approach opens up new avenues to solve robust and data-based problems arising in control, learning, finance, and other fields.