Stochastic Integer Programming: Limit Theorems and Confidence Intervals

Abstract

We consider empirical approximations (sample average approximations) of two-stage stochastic mixed-integer linear programs and derive central limit theorems for the objectives and optimal values. The limit theorems are based on empirical process theory and the functional delta method. We also show how these limit theorems can be used to derive confidence intervals for optimal values via resampling methods (bootstrap, subsampling).

Quantitative stability of fully random mixed-integer two-stage stochastic programs

“…the surveys [11,12,21,22]), the available (quantitative) stability or statistical estimation results do not cover situations with stochastic costs (or prices) (cf. [7,18,19]). …”

Multistep stochastic mirror descent for risk-averse convex stochastic programs based on extended polyhedral risk measures

“…The paper [5] deals more specifically with the computation of asymptotic confidence intervals for the optimal value of risk-neutral multistage stochastic programs. These results were extended to some stochastic programs with integer recourse in [17] and [8].…”

Uma proposta de modelagem para o cálculo de reservas de contingência e gerencial em projetos de software usando programação linear inteira estocástica DOI 10.5752/P.2316-9451.2012v1n1p50

“…Muitos modelos têm sido utilizados na literatura para tratar com incertezas, dentre eles podemos citar os modelos de programação estocástica (EICHHORN;RöMISCH, 2007), programação robusta (BEN-TAL; GHAOUI; NEMIROVSKI, 2006) e otimização fuzzy (LODWICK; KAC-PRZYK, 2010). Neste trabalho, iremos utilizar um modelo de programação inteira estocástica.…”