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This paper is concerned with objective value performance of the scenarioapproach for robust convex optimization. A novel method is proposed to deriveprobabilistic bounds for the objective value from scenario programs with afinite number of samples. This method relies on a max-min reformulation and theconcept of complexity of robust optimization problems. With additionalcontinuity and regularity conditions, via sensitivity analysis, we also provideexplicit bounds which outperform an existing result in the literature. Toillustrate the improvements of our results, we also provide a numericalexample.

Probabilistic guarantees on the objective value for the scenario approach via sensitivity analysis