We describe strong convex valid inequalities for conic quadratic mixed 0–1 optimization. These inequalities can be utilized for solving numerous practical nonlinear discrete optimization problems from value-at-risk minimization to queueing system design, from robust interdiction to assortment optimization through appropriate conic quadratic mixed 0–1 relaxations. The inequalities exploit the submodularity of the binary restrictions and are based on the polymatroid inequalities over binaries for the diagonal case. We prove that the convex inequalities completely describe the convex hull of a single conic quadratic constraint as well as the rotated cone constraint over binary variables and unbounded continuous variables. We then generalize and strengthen the inequalities by incorporating additional constraints of the optimization problem. Computational experiments on mean-risk optimization with correlations, assortment optimization, and robust conic quadratic optimization indicate that the new inequalities strengthen the convex relaxations substantially and lead to significant performance improvements.
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Entropic Value-at-Risk Constrained Optimal Power Flow Considering Distribution Network Outages During Extreme Events
Measuring and managing the risk of extensive distribution network outages during extreme events is critical for ensuring system-level energy balance in transmission network operations. However, existing risk measures used in stochastic optimization of power systems are computationally intractable for this problem involving large numbers of discrete random variables. Using a new coherent risk measure, Entropic Value-at-Risk (EVaR), that requires significantly less computational complexity, we propose an EVaR-constrained optimal power flow model that can quantify and manage the outage risk of extensive distribution feeders. The optimization problem with EVaR constraints on discrete random variables is equivalently reformulated as a conic programming model, which allows the problem to leverage the computational efficiency of conic solvers. The superiority of the proposed model is validated on the real-world Puerto Rico transmission grid combined with its large-scale distribution networks.
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- Award ID(s):
- 2103754
- PAR ID:
- 10610271
- Publisher / Repository:
- Institute of Electrical and Electronics Engineers (IEEE)
- Date Published:
- Journal Name:
- IEEE Transactions on Power Systems
- Volume:
- 40
- Issue:
- 1
- ISSN:
- 0885-8950
- Page Range / eLocation ID:
- 1184 to 1187
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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