Successive Quadratic Upper-Bounding for Discrete Mean-Risk Minimization and Network Interdiction
Abstract
The advances in conic optimization have led to its increased utilization for modeling data uncertainty. In particular, conic mean-risk optimization gained prominence in probabilistic and robust optimization. Whereas the corresponding conic models are solved efficiently over convex sets, their discrete counterparts are intractable. In this paper, we give a highly effective successive quadratic upper-bounding procedure for discrete mean-risk minimization problems. The procedure is based on a reformulation of the mean-risk problem through the perspective of its convex quadratic term. Computational experiments conducted on the network interdiction problem with stochastic capacities show that the proposed approach yields solutions within 1-2% of optimality in a small fraction of the time required by exact search algorithms. We demonstrate the value of the proposed approach for constructing efficient frontiers of flow-at-risk vs. interdiction cost for varying confidence levels.
Cite
@article{arxiv.1708.02371,
title = {Successive Quadratic Upper-Bounding for Discrete Mean-Risk Minimization and Network Interdiction},
author = {Alper Atamturk and Carlos Deck and Hyemin Jeon},
journal= {arXiv preprint arXiv:1708.02371},
year = {2018}
}