Abstract:

This paper deals with the lower bound of the radius of the robust feasibility for a class of convex optimization problems with uncertain convex polynomial constraints. Following the idea due to robust optimization, we first introduce the robust counterpart of the uncertain convex optimization problem and give the concept of radius of robust feasibility. By using the so-called epigraphical set and the Minkowski functions generated by the uncertain sets, we obtain the lower bound for the radius of robust feasibility of the uncertain convex optimization. Furthermore, an exact formula for the radius of the robust feasibility for an uncertain optimization problem with SOS-convex polynomial constraints is obtained. Our results extend and improve the corresponding results obtained in [10].

Key words: Polynomial constraints, Robust feasibility, Minkowski functions