Title: Simple yet Effective Approximations for Optimization Under Uncertainty
Abstract: In this talk, we present a novel and simple modeling method called harmonizing optimization (HO), which integrates Sample Average Approximation and Distributionally Robust Optimization with moment by adaptively adjusting the weights of data and information based on sample size N. This allows HO to amplify data effects in large samples while emphasizing information in smaller ones. Moreover, we provide practical methods for determining these weights and demonstrate that HO offers finite-sample performance guarantee. As an application, HO can be used to enhance scenario reduction by retaining critical information from reduced scenarios, thereby improving approximation quality and reducing completion time. Numerical results show significant advantages of HO in solution quality compared to other benchmark modeling approaches, and highlight its effectiveness in scenario reduction.