epigraphical convergence – Optimization Online

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

Published: 2025/09/26

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

Epi-convergence of Sample Averages of a Random Lower Semi-continuous Functional Generated by a Markov Chain and Application to Stochastic Optimization

Published: 2020/04/21

John Birge

Arnab Sur

Stochastic Programming asymptotic normality, consistency, epigraphical convergence, harris recurrent markov chain, measure-preserving ergodic transformation, random lower semi-continuous function, sample average approximation method

The purpose of this article is to establish epigraphical convergence of the sample averages of a random lower semi-continuous functional associated with a Harris recurrent Markov chain with stationary distribution $\pi$. Sample averages associated with an ergodic Markov chain with stationary probability distribution will epigraphically converge from $\pi$-almost all starting points. The property of Harris … Read more