Monte Carlo sampling methods

A Shapiro - Handbooks in operations research and management …, 2003 - Elsevier
In this chapter we discuss Monte Carlo sampling methods for solving large scale stochastic
programming problems. We concentrate on the “exterior” approach where a random sample …

Stability of stochastic programming problems

W Römisch - Handbooks in operations research and management …, 2003 - Elsevier
The behaviour of stochastic programming problems is studied in case of the underlying
probability distribution being perturbed and approximated, respectively. Most of the …

Learning models with uniform performance via distributionally robust optimization

JC Duchi, H Namkoong - The Annals of Statistics, 2021 - projecteuclid.org
Learning models with uniform performance via distributionally robust optimization Page 1 The
Annals of Statistics 2021, Vol. 49, No. 3, 1378–1406 https://doi.org/10.1214/20-AOS2004 © …

Statistics of robust optimization: A generalized empirical likelihood approach

JC Duchi, PW Glynn… - Mathematics of Operations …, 2021 - pubsonline.informs.org
We study statistical inference and distributionally robust solution methods for stochastic
optimization problems, focusing on confidence intervals for optimal values and solutions that …

[LIVRE][B] Lectures on stochastic programming: modeling and theory

This is a substantial revision of the previous edition with added new material. The
presentation of Chapter 6 is updated. In particular the Interchangeability Principle for risk …

[LIVRE][B] Introduction to stochastic programming

JR Birge, F Louveaux - 2011 - books.google.com
The aim of stochastic programming is to find optimal decisions in problems which involve
uncertain data. This field is currently develo** rapidly with contributions from many …

[LIVRE][B] Set-valued analysis

JP Aubin, JP Aubin - 1999 - Springer
Set-Valued Analysis Page 1 5 Set-Valued Analysis Introduction This chapter relates the
notions of mutations with the concept of gmphical derivatives of set-valued maps and more …

[LIVRE][B] Theory of random sets

I Molchanov, IS Molchanov - 2005 - Springer
Stochastic geometry is a relatively new branch of mathematics. Although its predecessors
such as geometric probability date back to the 18th century, the formal concept of a random …

Monte Carlo bounding techniques for determining solution quality in stochastic programs

WK Mak, DP Morton, RK Wood - Operations research letters, 1999 - Elsevier
A stochastic program SP with solution value z∗ can be approximately solved by sampling n
realizations of the program's stochastic parameters, and by solving the resulting …

Robust sample average approximation

D Bertsimas, V Gupta, N Kallus - Mathematical Programming, 2018 - Springer
Sample average approximation (SAA) is a widely popular approach to data-driven decision-
making under uncertainty. Under mild assumptions, SAA is both tractable and enjoys strong …