Optimization Online


Data-Driven Chance Constrained Programs over Wasserstein Balls

Zhi Chen (zhi.chen***at***imperial.ac.uk)
Daniel Kuhn (daniel.kuhn***at***epfl.ch)
Wolfram Wiesemann (ww***at***imperial.ac.uk)

Abstract: We provide an exact deterministic reformulation for data-driven chance constrained programs over Wasserstein balls. For individual chance constraints as well as joint chance constraints with right-hand side uncertainty, our reformulation amounts to a mixed-integer conic program. In the special case of a Wasserstein ball with the $1$-norm or the $\infty$-norm, the cone is the nonnegative orthant, and the chance constrained program can be reformulated as a mixed-integer linear program. Using our reformulation, we show that two popular approximation schemes based on the conditional-value-at-risk and the Bonferroni inequality can perform poorly in practice and that these two schemes are generally incomparable with each other.

Keywords: Distributionally robust optimization, ambiguous chance constraints, Wasserstein distance.

Category 1: Robust Optimization

Category 2: Stochastic Programming

Category 3: Integer Programming ((Mixed) Integer Nonlinear Programming )


Download: [PDF]

Entry Submitted: 06/22/2018
Entry Accepted: 06/22/2018
Entry Last Modified: 08/31/2018

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society