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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…
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…
Lagrangian dual with zero duality gap that admits decomposition
Diego Cifuentes, Santanu S. Dey, Jingye Xu
For mixed integer programs (MIPs) with block structures and coupling constraints, on dualizing the coupling constraints the resulting Lagrangian relaxation becomes decomposable int…
Branching with a pre-specified finite list of -sparse split sets for binary MILPs
Santanu S. Dey, Diego Moran, Jingye Xu
When branching for binary mixed integer linear programs with disjunctions of sparsity level , we observe that there exists a finite list of -sparse disjunctions, such that an…
Sensitivity analysis for mixed binary quadratic programming
Diego Cifuentes, Santanu S. Dey, Jingye Xu
We consider sensitivity analysis for Mixed Binary Quadratic Programs (MBQPs) with respect to changing right-hand-sides (rhs). We show that even if the optimal solution of a given M…