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Successive Quadratic Upper-Bounding for Discrete Mean-Risk Minimization and Network Interdiction

Alper Atamturk(atamturk***at***berkeley.edu)
Carlos Deck(cgdeck***at***berkeley.edu)
Hyemin Jeon(hyemin.jeon***at***berkeley.edu)

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.

Keywords: Risk, polymatroids, conic integer optimization, quadratic optimization, stochastic network interdiction

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Robust Optimization

Citation: BCOL Research Report 17.05, IEOR, UC Berkeley

Download: [PDF]

Entry Submitted: 12/30/2018
Entry Accepted: 12/30/2018
Entry Last Modified: 12/30/2018

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