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math.OC2026
Probabilistic analysis of dual decomposition on two-stage stochastic integer programs
Santanu S. Dey, Marco Molinaro, Jingye Xu
Two-stage stochastic integer programs provide a powerful framework for modeling decision-making under uncertainty, but they are notoriously difficult to solve at scale due to their…
math.OC2026
Asymptotically tight Lagrangian dual of smooth nonconvex problems via improved error bound of Shapley-Folkman Lemma
Santanu S Dey, Jingye Xu
In convex geometry, the Shapley-Folkman Lemma asserts that the nonconvexity of a Minkowski sum of dimensional bounded nonconvex sets does not accumulate once the number of summ…