probability functions – Optimization Online

Lipschitz Gradient Guarantees for Probability Functions and a New Algorithm for Probability Maximization

Published: 2026/05/29

Stochastic Programming probability functions, probability maximization, stochastic optimization, variational analysis

This work studies probability functions that appear in stochastic programming models. Although their differentiability has been widely investigated, the Lipschitz continuity of their gradients, crucial for the design and analysis of modern optimization algorithms, has received little attention. We develop a general framework that ensures differentiability and gradient Lipschitz continuity under practical conditions. Our framework … Read more

Approximating inequality systems within probability functions: studying implications for problems and consistency of first-order information

Published: 2025/09/26

Wim van Ackooij

Pedro Pérez-Aros

David Villacís

Nonsmooth Optimization, Stochastic Programming epigraphical convergence, nonsmooth analysis, probability functions, stochastic programming, variational analysis

In this work, we are concerned with the study of optimization problems featuring so-called probability or chance constraints. Probability constraints measure the level of satisfaction of an underlying random inequality system and ensure that this level is high enough. Such an underlying inequality system could be expressed by an abstractly known or perhaps costly to … Read more