Sequential Randomized Algorithms for Robust Convex Optimization

Sequential randomized algorithms are considered for robust convex optimization which minimizes a linear objective function subject to a parameter dependent convex constraint. Employing convex optimization and random sampling of parameter, these algorithms enable us to obtain a suboptimal solution within reasonable computational time. The suboptimal solution is feasible in a probabilistic sense and the suboptimal value belongs to an interval which contains the optimal value. The maximum of the interval is the optimal value of the robust convex optimization plus a specified tolerance. On the other hand, its minimum is the optimal value of the chance constrained optimization which is a probabilistic relaxation of the robust convex optimization, with high probability.