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

2022/04/19 by Zheming Wang, Raphaël M. Jungers, Wang, Zheming +1
Decision Sciences · Engineering · #FOS: Mathematics #Optimization and Control (math.OC) #Probabilistic and Robust Engineering Design #Risk and Portfolio Optimization #Water resources management and optimization

paper · pdf · doi:10.48550/arxiv.2204.08733

openalex publication_date 2022/04/19 · openalex created_date 2022/04/26 · openalex updated_date 2026/07/28

Abstract

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.

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