The IEOR Department is pleased to host an invited research seminar by Prof. Santanu Dey (Georgia Tech) on 31 July 2026, from 12:00 PM to 1:00 PM at the IEOR Seminar Room.
Title: Strong Lagrangian Duals that Still Decompose: Exact Encodings and Learned Proxies
Abstract: For block-structured mixed-integer optimization problems, Lagrangian decomposition buys separability of the subproblems at the price of a duality gap. This talk shows how to recover both properties at once, by adding redundant constraints that are nonlinear but separable across blocks and then dualizing them.
For binary coupling variables, two families of encodings, monomials and indicators of binary points, give a Lagrangian dual with zero duality gap while every subproblem stays independent, at the cost of nonlinear subproblem objectives and possibly exponentially many multipliers. The argument uses no linearity, so it covers MINLPs, and extends to the blocks of any tree decomposition. We report computations with a branch-cut-and-price scheme that separates encoding terms dynamically. When the encoding is only learned, a proxy whose error against an extended response function is uniformly bounded gives a valid dual bound whose distance from optimal is at most twice that bound. The relaxation splits into an estimation problem of the Neur2SP type and a new correction problem that converts it into a dual bound. Joint work with Gustavo Angulo, Diego Cifuentes, Shaoze Wang, and Jingye Xu.