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ARC-TRIAD
Cong Han Lim (Wisconsin)
Wednesday, January 17, 2018
Groseclose 402 - 10:00 am
Title: Towards Large-Scale Nonconvex/Stochastic Discrete Optimization
Abstract: Modern data analytics is powered by scalable mathematical optimization methods. For decision-making, we want to be able to solve large-scale mathematical problems that include discrete choices or structures. These can already be very challenging to solve exactly even when the objective and feasible region are convex. We want to be able to model more general concepts that naturally lead to huge or nonconvex formulations, such as robustness to uncertainty, economic ideas like economies of scale, and physical concepts in engineering applications such as power systems and water network design.
In this talk, I will present techniques for handling two such families of problems. I will demonstrate a new class of cutting planes for mixed-integer programs with separable concave costs and show that they can be combined with existing cuts for canonical mixed-integer linear sets. For stochastic mixed-integer programs, I will describe a new subgradient method for solving the dual decomposition that parallelizes significantly better than traditional subgradient on modern distributed and multi-core computer architectures. I will conclude by discussing some future directions in machine learning and (stochastic) mixed-integer programming.
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