Optimization Online


A Tractable Approach for designing Piecewise Affine Policies in Two-stage Adjustable Robust Optimization

Aharon Ben-Tal (abental***at***ie.technion.ac.il)
Omar El Housni (oe2148***at***columbia.edu)
Vineet Goyal (vg2277***at***columbia.edu)

Abstract: We consider the problem of designing piecewise affine policies for two-stage adjustable robust linear optimization problems under right-hand side uncertainty. It is well known that a piecewise affine policy is optimal although the number of pieces can be exponentially large. A significant challenge in designing a practical piecewise affine policy is constructing good pieces of the uncertainty set. Here we address this challenge by introducing a new framework in which the uncertainty set is ``approximated'' by a ``dominating'' simplex. The corresponding policy is then based on a mapping from the uncertainty set to the simplex. Although our piecewise affine policy has exponentially many pieces, it can be computed efficiently by solving a compact linear program given the dominating simplex. Furthermore, we can find the dominating simplex in a closed form if the uncertainty set satisfies some symmetries and can be computed using a MIP in general. The performance of our policy is significantly better than the affine policy for many important uncertainty sets, such as ellipsoids and norm-balls, both theoretically and numerically. For instance, for hypersphere uncertainty set, our piecewise affine policy can be computed by an LP and gives a $O(m^{1/4})$-approximation whereas the affine policy requires us to solve a second order cone program and has a worst-case performance bound of $O(\sqrt m)$.

Keywords: Robust Optimization, Adaptive Optimization, Approximation algorithms

Category 1: Robust Optimization

Citation: Submitted to Math Programming

Download: [PDF]

Entry Submitted: 07/24/2016
Entry Accepted: 07/24/2016
Entry Last Modified: 01/20/2018

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