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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…
Accelerating Column Generation in Highly Degenerate Integer Programming Problems with Template Pricing
Luke Marshall, Prachi Shah, Santanu S. Dey
We propose a new pricing strategy for column generation (CG), referred to as Template pricing. This method is motivated by the desire to coordinate solutions of different pricing s…
Chvátal-Gomory Rounding of Eigenvector Inequalities for QCQPs
Santanu S. Dey, Nan Jiang, Aleksandr Kazachkov +2
We introduce and analyze a class of valid inequalities for nonconvex quadratically constrained optimization problems (QCQPs) which we call Eigen-CG inequalities. These inequalities…
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…
Strengthening Dual Bounds for Multicommodity Capacitated Network Design with Unsplittable Flow Constraints
Lacy M. Greening, Santanu S. Dey, Alan L. Erera
Multicommodity capacitated network design (MCND) models can be used to optimize the consolidation of shipments within e-commerce fulfillment networks. In practice, fulfillment netw…
Extreme Strong Branching for QCQPs
Santanu S. Dey, Dahye Han, Yang Wang
For mixed-integer programs (MIPs), strong branching is a highly effective variable selection method to reduce the number of nodes in the branch-and-bound algorithm. Extending it to…