stochastic optimization

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.
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
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.
Thursday, March 29, 2012 - 5:30pm - 6:15pm
Nathan (Nati) Srebro (Toyota Technological Institute at Chicago)
I will discuss deep connections between Statistical Learning, Online
Learning and Optimization. I will show that there is a tight
correspondence between the sample size required for learning and the
number of local oracle accesses required for optimization, and the
same measures of complexity (e.g. the fat-shattering dimension or
Rademacher complexity) control both of them. Furthermore, I will show
how the Mirror Descent method, and in particular its stochastic/online
variant, is in a strong sense universal for online learning,
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