  This paper is concerned with objective value performance of the scenario
approach for robust convex optimization. A novel method is proposed to derive
probabilistic bounds for the objective value from scenario programs with a
finite number of samples. This method relies on a max-min reformulation and the
concept of complexity of robust optimization problems. With additional
continuity and regularity conditions, via sensitivity analysis, we also provide
explicit bounds which outperform an existing result in the literature. To
illustrate the improvements of our results, we also provide a numerical
example.
