Randomized algorithms for robust feasibility problems with general nonconvex constraints

A class of robust feasibility problems is considered, which is to find a design variable satisfying a parameter- dependent constraint for all parameter values. A randomized algorithm for solving the problem with a general nonconvex constraint is proposed, where random samples of candidates of the design variable and uncertain parameters are used. The algorithm stops in a finite number of iterations. Then, it gives a design variable satisfying the constraint for almost all parameter values with a prescribed confidence or says that the problem is infeasible in a probabilistic sense.