Scenario Approach to Probabilistic Design

This chapter describes a non-sequential randomized technique for achieving probabilistic robustness in design. For problems where the performance function is convex in the design parameters, the simple idea of scenario design is to use a finite number of random samples of the uncertainty (the scenarios) to construct a standard convex optimization problem that can then be solved efficiently to obtain the desired design. The key feature of scenario theory, however, is to derive a rigorous probabilistic reliability certificate for the obtained design. The fundamental results of scenario theory are presented, together with extensions pertaining to scenario optimization with violated constraints and relations between scenario optimization and chance-constrained optimization.