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Numerical analysis

Summer school 2012

Stochastic Optimization

Cadarache, from June 25 till July 6, 2012.
Logo CEA


Michel De Lara (CERMICS) and Stéphane Gaubert (INRIA)


Abstract

This school will cover three approaches in stochastic optimization — stochastic programming, dynamic programming, variational methods — by emphasizing the modelling of dynamical control problems, as well as algorithmics aspects. Among the applications, we find the management of energy systems under uncertainty.

 

Contents

1 Place, Dates, Public
2 Main Courses
  • 2.1 Stochastic Programming (Roger Wets)
  • 2.2 Large-Scale Approximate Dynamic Programming and Reinforcement Learning (Dimitri Bertsekas)
  • 2.3 Information Constraints in Stochastic Control (Pierre Carpentier, Jean-Philippe Chancelier, Michel De Lara)
1. Place, Dates, Public
Accommodation and courses take place in a castle depending of the CEA (French AlternativeEnergies and Atomic Energy Commission) at Cadarache, South of France, from Monday,June 25th till Friday, July 6th, 2012.
These courses can interest a public of industrial engineers as well as academics (in particular researchers from CEA, EDF and INRIA), confirmed or not, in particular the PhDand the post-doctorate students.

 

2. Main Courses
Stochastic optimization will be approached under three angles
    • Stochastic Programming
    • Dynamic Programming
    • Variational Methods
corresponding to different ways to handle non-anticipativity constraints, and leading to different resolution methods. Each course lasts 9 hours and comprises six sessions of 1h30.
Computer practical works and “practical lectures” alternate with the theoretical courses and are organized in 3 (or 4) sessions of 2 hours each.

2.1 Stochastic Programming (Roger Wets)

1. Deterministic versus stochastic models? Different criteria when having to cope with uncertainty

2. Stochastic programs with recourse: from simple to extensive dynamic models

3. Duality theory: the role of induced constraints and non-anticipativity constraints

4. Solution procedures: Decomposition methods and Progressive Hedging

5. Approximation Issues, Sampling and Laws of Large Numbers

6. Stochastic programs with chance constraints: motivation, approximations, solution Procedures

7. Integer stochastic programming: heuristics , bounds

Computer practical works (Luis Fernando Solaris) :

TP1. Formulation/solution of simple stochastic programs

TP2-3. Introduction to the scientific software Pyomo. Formulation (solution) of a hydro-electric power generation problem

TP4. The unit commitment problem (ISO), i.e., dynamic mixed-integer stochastic program.

2.2 Large-Scale Approximate Dynamic Programming and Reinforcement Learning (Dimitri Bertsekas)

1. Infinite Horizon Dynamic Programming (DP)

2. Computational Methods for DP

3. Large-Scale DP: General Issues

4. Approximate Policy Iteration and Temporal Difference Methods

5. Projection Methods, Aggregation Methods, and Q-Learning

6. DP and Monte-Carlo Linear Algebra

Practical lectures (Mengdi Wang – MIT) :

TP1. Theory and computational methods of exact DP

TP2. Theory and computational methods of approximate DP

TP3. Approximate policy iteration methods, and Q-Learning

2.3 Information Constraints in Stochastic Control (Pierre Carpentier, Jean-Philippe Chancelier, Michel De Lara)

1. Introduction to information constraints and discretization puzzles in stochastic control.
Mathematical representations of information constraints. (MDL)

2. First-order optimality conditions and variational approach to stochastic control: theory. (PC)

3. First-order optimality conditions and variational approach to stochastic control: algorithms. (PC)

4. Decomposition-coordination methods under information constraints. (PC)

5. Probability constraints and dynamic consistency. (JPC)

6. Introduction to multi-agent decentralized optimization. (MDL)

Computer practical works (Pierre Carpentier, Jean-Philippe Chancelier, Michel De Lara):

TP1. Dynamic programming for a single dam

TP2. Dam management under probability constraint

TP3. Decomposition-coordination methods for interconnected dams

 

Reminder:
Summer schools are intended for researchers, engineers and PhD students.

They allow them to review the state of progress of the proposed subjects and to confront their experience.

The teaching is done in English. It is complemented by practical works, in small groups, hosted by assistants.

Registration:

If you wish to join, thank you for filling this registration form and sending it to Régis Vizet before may 30, 2012

 

Contacts:

Summer Schools secretary
Régis Vizet - CEA
tel: 01 69 26 47 45
Fax: 01 69 26 70 80


Coordinators of the numerical analysis summer school:

Registration fees:
Full rate: 2800 euros
Academia/ University & Public Research rate: 1400 euros
Phd student rate: 700 euros
(accommodation and meals included)

Grant application:

A limited number of young researchers (PhD students, postdocs) will be offered to cover registration fees.
In order to apply, please send an e-mail to the scientific organizers (S. Gaubert and M. De Lara) at the earliest, and no later than April 15 2012, including:
  • your CV
  • the contact details of at least one referee (no letter of reference required)
  • a letter of motivation addressed to the organizers stating how you expect to benefit from your participation.
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This event is partially supported by the Marie-Curie Initial training network SADCO
(«FP7-PEOPLE-2010-ITN», Grant agreement number 264735-SADCO)