Mini Courses - SVAN 2016


Youtube Playlist: LINK


Mini Course 1 -
Scenario Generation And Sampling Methods

Güzin Bayraksan - Ohio State University, USA

Tito Homem-de-Mello - University Adolfo Ibáñez, Chile

We review methods for generating scenarios to approximate stochastic optimization problems. General methods such as Monte Carlo, Latin hypercube sampling and quasi-Monte Carlo methods will be discussed.  We will provide an overview of properties of such methods, in terms of asymptotic convergence and behavior for finitely many samples. We will also review a number of specialized sequential sampling algorithms to solve stochastic optimization problems and methods to assess solution quality. In the context of multi-stage stochastic programs, we will pay particular attention to methods for generating scenario trees, such as moment-matching, clustering, and probability-based metrics. We will discuss applications of the methods studied in the course, especially  in the areas of energy and finance.

Material

Homem-de-Mello, T. and Bayraksan, G., “Monte Carlo Sampling-Based Methods for Stochastic Optimization,Surveys in Operations Research and Management Science, 19(1): 56–85, 2014 [www]

Session 1: pdf,  Session 2: pdfSession 3: pdfSession 4: pdfSession 5: pdf

DOWNLOAD

MC1 
Class 01
- 09-05-2016 - download
Class 02 - 09-05-2016 - download
Class 03 - 11-05-2016 - download
Class 04 - 11-05-2016 - download
Class 05 - 11-05-2016 - download
Class 06 - 13-05-2016 - download
Class 07 - 13-05-2016 - download
Class 08 - 13-05-2016 - download


Mini Course 2 - Equilibrium Routing Under Uncertainty

Roberto Cominetti, University Adolfo Ibáñez, Chile

We review several alternative models that have been used to describe traffic in congested networks, both in urban transport and telecommunications. We focus on situations where travel times are subject to random fluctuations and how this variability affects the traffic flows. We consider both atomic and non-atomic equilibrium models, and we discuss a class of adaptive dynamics that describe the behavior of agents and which provides a plausible micro-foundation for the emergence of equilibrium. We also discuss some recent ideas on how risk aversion to random travel times might be incorporated in the models. In our presentation we use convex optimization to provide a unifying framework for the different concepts of equilibrium.

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MC2
Class 01 - 16-05-2016 - download
Class 02 - 17-05-2016 - download
Class 03
- 18-05-2016 - download
Class 04
- 19-05-2016 - download

Mini Course 3 -

Stochastic Convex Optimization Methods In Machine Learning



Mark Schmidt, University of British Columbia

We first review classic algorithms and complexity results for stochastic methods for convex optimization, and then turn our attention to the wide variety of exponentially-convergent algorithms that have been developed in the last four years. Topics will include finite-time convergence rates of classic stochastic gradient methods, stochastic average/variance-reduced gradient methods, primal-dual methods, proximal operators, acceleration, alternating minimization, non-uniform sampling, and a discussion of parallelization and non-convex problems. Applications in the field of machine learning will emphasized, but the principles we cover in this course are applicable to many fields.

Material
L1, L2, L3, L4, L5a, L5b, L6, L7, L8

DOWNLOAD

MC3
Class 01 - 16-05-2016 - download
Class 02 - 16-05-2016 - download
Class 03 - 17-05-2016 - download
Class 04 - 18-05-2016 - download
Class 05 - 18-05-2016 - download
Class 06 - 19-05-2016 - download
Class 07 - 20-05-2016 - download
Class 08 - 20-05-2016 - download


Mini Course 4 - Stochastic Variational Inequalities, Optimization And Risk

R. Tyrrell Rockafellar - University of Washington and University of Florida, USA

These introductory lectures will be devoted to Stochastic Variational Inequalities, and RIsk, Optimization and Statistics.

DOWNLOAD

MC4
Class 01 - 21-06-2016 - download
Class 02 - 22-06-2016 - download
Class 03 - 23-06-2016 - download

Mini Course 5 - Stochastic Optimal Control

Hasnaa Zidani, Ensta-ParisTech, France

This course will be dedicated to optimal control problems with some applications in economics and energy management. 
These stochastic optimization problems will be addressed by a dynamic programming approach that characterizes the value function as solution to a partial differential equation, called Hamilton-Jacobi equation. 
We will first discuss the properties of the function value and its role in deriving the optimal policy. 
Then we will see some numerical methods for solving the control problems.

DOWNLOAD

MC5
Class 01 - 20-06-2016 - download
Class 02 - 21-06-2016 - download
Class 03 - 22-06-2016 - download
Class 04 - 22-06-2016 - download
Class 05 - 24-06-2016 - download

Special Conference - Stochastic Variational Inequalities in a Dynamical Framework

Most of the research on stochastic variational inequalities has concentrated on models in which information about the uncertain future is revealed only once.

Such models are inadequate to cover multistage stochastic programming, where information comes in stages that offer repeated opportunities for recourse decisions.

That feature can be brought into stochastic variational inequalities by adapting them to a constraint of nonanticipativity.

In that way not only stochastic programming but multistage multiagent games can be covered. 

A particular advantage of this approach is that it generates information price vectors which can be used to decompose the overall problem into a separate problem for each scenario.

This fits with solution approaches like the progressive hedging algorithm.

DOWNLOAD

22-06-2016 - download

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