Rockafellian Relaxation and Stochastic Optimization Under Perturbations

Johannes O. Royset (), Louis L. Chen () and Eric Eckstrand ()
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Johannes O. Royset: Industrial and Systems Engineering, University of Southern California, Los Angeles, California 90007
Louis L. Chen: Operations Research, Naval Postgraduate School, Monterey, California 93943
Eric Eckstrand: Operations Research, Naval Postgraduate School, Monterey, California 93943

Mathematics of Operations Research, 2025, vol. 50, issue 3, 1585-1610

Abstract: 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 two-stage 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 Phi-divergence, 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.

Keywords: 90C15 Stochastic programming; 90C26 Nonconvex programming; global optimization; duality theory; nonlinear programming; optimality conditions; stochastic programming; sensitivity (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:50:y:2025:i:3:p:1585-1610

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