Gradients and Subgradients of Buffered Failure Probability
This work addresses a technical challenge in optimization theory for researchers and practitioners dealing with reliability and risk analysis, but it appears incremental as it builds on existing subdifferential calculus.
The paper tackles the problem of computing gradients and subgradients for buffered failure probabilities, which are crucial in optimization and sensitivity analysis, by providing characterizations for finite distributions and gradient expressions under certain assumptions, with examples demonstrating their use in optimality conditions.
Gradients and subgradients are central to optimization and sensitivity analysis of buffered failure probabilities. We furnish a characterization of subgradients based on subdifferential calculus in the case of finite probability distributions and, under additional assumptions, also a gradient expression for general distributions. Several examples illustrate the application of the results, especially in the context of optimality conditions.