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Data-Driven Two-Stage Conic Optimization with Rare High-Impact Zero-One Uncertainties

Anirudh Subramanyam (asubramanyam***at***anl.gov)
Mohamed El Tonbari (mtonbari***at***gatech.edu)
Kibaek Kim (kimk***at***anl.gov)

Abstract: We address high dimensional zero-one random parameters in two-stage convex conic optimization problems. Such parameters typically represent failures of network elements and constitute rare, high-impact random events in several applications. Given a sparse training dataset of the parameters, we motivate and study a distributionally robust formulation of the problem using a Wasserstein ambiguity set centered at the empirical distribution. We present a simple, tractable and conservative approximation of this problem that can be efficiently computed and iteratively improved. Our method relies on a reformulation that optimizes over the convex hull of a mixed-integer conic programming representable set, followed by an approximation of this convex hull using lift-and-project techniques. We illustrate the practical viability and strong out-of-sample performance of our method on nonlinear optimal power flow problems affected by random contingencies, and report improvements of up to 20\% over existing methods.

Keywords: Distributionally robust optimization, conic optimization, rare events, two-stage problems

Category 1: Robust Optimization

Category 2: Stochastic Programming

Citation:

Download: [PDF]

Entry Submitted: 01/01/2020
Entry Accepted: 01/01/2020
Entry Last Modified: 01/14/2020

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