Rockafellian Relaxation and Stochastic Optimization Under Perturbations

• 成果类型: Article
• 署名作者: Royset, Johannes O.; Chen, Louis L.; Eckstrand, Eric
• 署名单位: University of Southern California; United States Department of Defense; United States Navy; Naval Postgraduate School
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2022.0122
• 发表日期: 2025
• 关键词: robust; STABILITY; sensitivity; constraints; Duality; DESIGN

摘要

In practice, optimization models are often prone to unavoidable inaccuracies because of dubious assumptions and corrupted data. Traditionally, this placed special emphasis on risk-based and robust formulations, and their focus on conservative decisions. We develop, in contrast, an optimistic framework based on Rockafellian relaxations in which optimization is conducted not only over the original decision space but also jointly with a choice of model perturbation. The framework enables us to address challenging problems with ambiguous probability distributions from the areas of twostage stochastic optimization without relatively complete recourse, probability functions lacking continuity properties, expectation constraints, and outlier analysis. We are also able to circumvent the fundamental difficulty in stochastic optimization that convergence of distributions fails to guarantee convergence of expectations. The framework centers on the novel concepts of exact and limit-exact Rockafellians, with interpretations of negative regularization emerging in certain settings. We illustrate the role of Phidivergence, examine rates of convergence under changing distributions, and explore extensions to first-order optimality conditions. The main development is free of assumptions about convexity, smoothness, and even continuity of objective functions. Numerical results in the setting of computer vision and text analytics with label noise illustrate the framework.