The wait-and-judge scenario approach applied to antenna array design

The scenario optimisation approach is a methodology for finding solutions to uncertain convex problems by resorting to a sample of data, which are called “scenarios”. In a min–max set-up, the solution delivered by the scenario approach comes with tight probabilistic guarantees on its risk defined as the probability that an empirical cost threshold will be exceeded when the scenario-based solution is adopted. While the standard theory of scenario optimisation has related the risk of the data-based solution to the number of optimisation variables, a more recent approach, called the “wait-and-judge” scenario approach, enables the user to assess the risk of the solution in a data-dependent way, based on the number of decisive scenarios (“support scenarios”). The aim of this paper is to illustrate the potentials of the wait-and-judge approach for min–max sample-based design and we shall consider to this purpose an antenna array design problem.