- A Tractable Approach for designing Piecewise Affine Policies in Two-stage Adjustable Robust Optimization Aharon Ben-Tal (abentalie.technion.ac.il) Omar El Housni (oe2148columbia.edu) Vineet Goyal (vg2277columbia.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: 07/24/2016Entry Accepted: 07/24/2016Entry Last Modified: 01/20/2018Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.