Fabrizio Dabbene In this paper, we consider multistage robust convex optimization problems of the minimax type. We approximate the given robust problem by a sampled subproblem, where instead of looking for the worst case among the infinite and typically uncountable set of uncertain parameters, we consider only the worst case among a randomly selected subset of parameters. … Read more
Many uncertainty sets encountered in control systems analysis and design can be expressed in terms of semialgebraic sets, that is as the intersection of sets described by means of polynomial inequalities. Important examples are for instance the solution set of linear matrix inequalities or the Schur/Hurwitz stability domains. These sets often have very complicated shapes … Read more
We propose a randomized method for general convex optimization problems; namely, the minimization of a linear function over a convex body. The idea is to generate N random points inside the body, choose the best one and cut the part of the body defined by the linear constraint. We first analyze the convergence properties of … Read more