# Stochastic programming

Tuesday, August 9, 2016 - 11:00am - 12:30pm

Jeff Linderoth (University of Wisconsin, Madison)

Continuing the first lecture, we will introduce advanced features that

improve the performance of algorithms for solving the Benders-based

decomposition. Aggregating scenarios and regularization approaches

will be a primary focus. We will also introduce a different dual

decomposition technique that can be effective for solving two-stage

stochastic programs, and discuss algorithmic approaches for solving

the dual decomposition.

improve the performance of algorithms for solving the Benders-based

decomposition. Aggregating scenarios and regularization approaches

will be a primary focus. We will also introduce a different dual

decomposition technique that can be effective for solving two-stage

stochastic programs, and discuss algorithmic approaches for solving

the dual decomposition.

Tuesday, August 9, 2016 - 2:00pm - 3:30pm

Shabbir Ahmed (Georgia Institute of Technology)

Multistage stochastic programming (MSP) is a framework for sequential decision making under uncertainty where the decision space is typically high dimensional and involves complicated constraints, and the uncertainty is modeled by a general stochastic process. In the traditional risk neutral setting, the goal is to find a sequence of decisions or a policy so as to optimize an expected value objective. MSP has found applications in a variety of important sectors including energy, finance, manufacturing, services, and natural resources.

Monday, August 8, 2016 - 9:00am - 10:30am

Jeff Linderoth (University of Wisconsin, Madison)

This lecture gives an introduction to modeling optimization

problems where parameters of the problem are uncertain. The primary

focus will be on the case when the uncertain parameters are modeled as

random variables. We will introduce both two-stage, recourse-based

stochastic programming and chance-constrained approaches. Statistics

that measure the value of computing a solution to the stochastic

problem will be introduced. We will show how to create

an equivalent extensive form formulations of the instances, so that

problems where parameters of the problem are uncertain. The primary

focus will be on the case when the uncertain parameters are modeled as

random variables. We will introduce both two-stage, recourse-based

stochastic programming and chance-constrained approaches. Statistics

that measure the value of computing a solution to the stochastic

problem will be introduced. We will show how to create

an equivalent extensive form formulations of the instances, so that

Tuesday, August 9, 2016 - 9:00am - 10:30am

Jim Luedtke (University of Wisconsin, Madison)

We present the Benders decomposition algorithm for solving two-stage stochastic optimization models. The main feature of this algorithm is that it alternates between solving a relatively compact master problem, and a set of subproblems, one per scenario, which can be solved independently (hence decomposing the large problem into many small problems). After presenting and demonstrating correctness of the basic algorithm, several computational enhancements will be discussed, including effective selection of cuts, multi-cut vs.

Monday, August 8, 2016 - 11:00am - 12:30pm

Jim Luedtke (University of Wisconsin, Madison)

This lecture introduces the concept of risk measures and their use in stochastic optimization models to enable decision makers to seek decisions that are less likely to yield a highly undesirable outcome. In particular, we focus on coherent and convex risk measures, and demonstrate the duality relationship between such risk measures and distributionally robust stochastic optimization models. The specific examples of average value-at-risk (also known as conditional value-at-risk) and mean semideviation risk measures will be presented.

Monday, October 18, 2010 - 3:00pm - 4:00pm

Werner Römisch (Humboldt-Universität)

First, three approaches to scenario generation besides

Monte Carlo methods are considered: (i) Optimal quantization

of probability distributions, (ii) Quasi-Monte Carlo

methods and (iii) Quadrature rules based on sparse

grids. The available theory is discussed and related

to applying them in stochastic programming. Second,

the problem of optimal scenario reduction and the

generation of scenario trees for multistage models

are addressed.

Monte Carlo methods are considered: (i) Optimal quantization

of probability distributions, (ii) Quasi-Monte Carlo

methods and (iii) Quadrature rules based on sparse

grids. The available theory is discussed and related

to applying them in stochastic programming. Second,

the problem of optimal scenario reduction and the

generation of scenario trees for multistage models

are addressed.

Tuesday, October 19, 2010 - 2:00pm - 3:00pm

Jean-Paul Watson (Sandia National Laboratories), David Woodruff (University of California)

Although stochastic programming is a powerful tool for modeling decision-making under uncertainty,

various impediments have historically prevented its widespread use. One key factor involves the

ability of non-experts to easily express stochastic programming problems, ideally building on a likely

existing deterministic model expressed through an algebraic modeling language. A second key factor

relates to the difficulty of solving stochastic programming models, particularly the general mixed-integer,

various impediments have historically prevented its widespread use. One key factor involves the

ability of non-experts to easily express stochastic programming problems, ideally building on a likely

existing deterministic model expressed through an algebraic modeling language. A second key factor

relates to the difficulty of solving stochastic programming models, particularly the general mixed-integer,