Jose Blanchet, Fan Zhang, Bert Zwart (2023) Efficient Scenario Generation for Heavy-Tailed Chance Constrained Optimization. Stochastic Systems 14(1):22-46.
https://doi.org/10.1287/stsy.2021.0021
Abstract
We consider a generic class of chance-constrained optimization problems with heavy-tailed (i.e., power-law type) risk factors. As the most popular generic method for solving chance constrained optimization, the scenario approach generates sampled optimization problem as a precise approximation with provable reliability, but the computational complexity becomes intractable when the risk tolerance parameter is small. To reduce the complexity, we sample the risk factors from a conditional distribution given that the risk factors are in an analytically tractable event that encompasses all the plausible events of constraints violation. Our approximation is proven to have optimal value within a constant factor to the optimal value of the original chance constraint problem with high probability, uniformly in the risk tolerance parameter. To the best of our knowledge, our result is the first uniform performance guarantee of this …
Authors
Jose Blanchet, Fan Zhang, Bert Zwart
Publication date
2024/3
Journal
Stochastic Systems
Volume
14
Issue
1
Pages
22-46
Publisher
INFORMS
