Bernard DrÃ©villon
prÃ©sentation
Bernard DrÃ©villon commence sa carriÃ¨re de recherche en Physique des Hautes Energies Ã lâ€™Ecole polytechnique en 1969. Il soutient sa thÃ¨se soutenue en 1973. Puis il se tourne vers la synthÃ¨se de couches minces de silicium pour applications photovoltaÃ¯ques et participe Ã la crÃ©ation du Laboratoire de Physique des Interfaces et des Couches Minces (LPICM) Ã lâ€™Ecole polytechnique en 1986. Il se spÃ©cialise dans une technique de caractÃ©risation optique originale (ellipsomÃ©trie spectroscopique) qui permet le suivi en temps rÃ©el de la croissance des couches. Lâ€™instrument sera ensuite exploitÃ©e commercialement par JobinYvon (devenue Horiba) Ã partir des annÃ©es 90. Plusieurs centaines dâ€™ellipsomÃ¨tres ont Ã©tÃ© vendus depuis dans le monde entier.
B. DrÃ©villon a dirigÃ© le LPICM de 1999 Ã 2012 et participÃ© activement Ã la crÃ©ation de lâ€™Institut PhotovoltaÃ¯que dâ€™Ile de France (IPVF, opÃ©rationnel en 2016), en collaboration avec EDF et TOTAL. B. DrÃ©villon est lâ€™auteur de plus de 250 publications dans des revues Ã comitÃ© de lecture (facteur H : 41) et dâ€™une trentaine de brevets dâ€™invention. Il a dirigÃ© plus de vingt thÃ¨ses. Il est Professeur Ã lâ€™Ã‰cole polytechnique depuis 2001, il dirige le Master Renewable Energy Science and Technology (REST) depuis 2011. Â Â
BIO653  Naturebased Solutions to Substitute Fossil Resources and Address Global Warming (20202021)
Naturebased solutions to substitute fossile resources and address global change
Lecturer: Benoît Gabrielle  AgroParisTech
Natural ecosystems and the services they provide are a key to address current environmental challenges, such as climate change, the preservation of air and water quality, and the transition toward a lowcarbon economy. Engineering these services via the management of ecosystems, landuse planning or the integration of plants in urban environments can « pave the way towards a more resource efficient, competitive and greener economy » (EU Research Agenda, 2015). Naturebased solutions include for example the production of biobased alternatives to fossilebased products, the mitigation of heat waves in cities via the presence of vegetation, the enhacement of carbon storage in ecosystems or the management of watersheds to reduce flood risks.
The aim of the course is to raise the awareness of these solutions, with a particular focus on biomass production and transformation into fuels, materials and chemicals to substitute fossile resources, and to equip them with key concepts and knowhows on the design and assessment of such solutions. The course will provide students with a detailed understanding of the issues associated with the development of naturebased solutions to meet our needs for food and energy, mitigate climate change or air pollution, and methods to their sustainability along the environmental and economic dimensions.
Langue du cours : Anglais
Credits ECTS : 4
Naturebased solutions to substitute fossile resources and address global change
Lecturer: Benoît Gabrielle  AgroParisTech
Natural ecosystems and the services they provide are a key to address current environmental challenges, such as climate change, the preservation of air and water quality, and the transition toward a lowcarbon economy. Engineering these services via the management of ecosystems, landuse planning or the integration of plants in urban environments can « pave the way towards a more resource efficient, competitive and greener economy » (EU Research Agenda, 2015). Naturebased solutions include for example the production of biobased alternatives to fossilebased products, the mitigation of heat waves in cities via the presence of vegetation, the enhacement of carbon storage in ecosystems or the management of watersheds to reduce flood risks.
The aim of the course is to raise the awareness of these solutions, with a particular focus on biomass production and transformation into fuels, materials and chemicals to substitute fossile resources, and to equip them with key concepts and knowhows on the design and assessment of such solutions. The course will provide students with a detailed understanding of the issues associated with the development of naturebased solutions to meet our needs for food and energy, mitigate climate change or air pollution, and methods to their sustainability along the environmental and economic dimensions.
Langue du cours : Anglais
Credits ECTS : 4
PHY630  Physics Refresher Course (20202021)
PHY698  Internship for Energy Environment II (20202021)
STEEM2 internships will start from the end of March and shall last 20 to 24 weeks (5 to 6 months).
A STEEM2 internship must be a research internship.
However, the word research can be appreciated quite widely. It is not necessarily academic research, it may be scientific, technical, industrial or economic research or development, but it is not an execution internship. Indeed, the internship must not consist of carrying out standard works, whether predefined or not, within a department; the internship must have a welldefined objective and must lead to the realization of an original deliverable: a software, an experiment, a study that can be scientific, statistical, economic .... but original!
There is also no restriction on the organization hosting you: academic lab. or company, from startup to large industrial group, or administration or paraadministrative body, in France or abroad (but this may cause visa problems).
Fundamentally what is important is to assess the managerial capacity of the host organization, how it can guide you in your research and what you can learn there.
When choosing your internship, think about what you plan to do the year after. Do you plan to begin a PhD, to find a job in a company, to launch a startup or anything else? There will be many opportunities for you, but some of them require a specific internship.
For an academic PhD prefer an internship in an academic lab, it may give you good references and even propose PhD opportunities. A thesis in a company is also conceivable, in this case favour rather important companies, small ones rarely have the means to support a PhD student.
For a future career in a company remember to become the real specialist they will need, the internship is there to train you in a specialty but also to give you the opportunity to prove your scientific and technical competences, often big or small companies use internships to test their future employers, it will be your last student exam so don’t miss it!
Whatever the type of internship you will choose, your ability to present the progress of your work and your results clearly and synthetically is also very important and may influence strongly your future. Therefore, the internship ends with a report and an oral defence, see on SynapseS the dedicated advices for these topics.
You will have to choose an internship at the end of December or during January, to this end you will benefit on the web of a lot of information:
 Dedicated proposals received for STEEM students will be posted.
 The list of internships done by STEEM, REST and WAPE students during the previous years.
 The Polytechnique Career Center internship proposals whatever the discipline.
 You may join the LINKEDIN group “Ecole Polytechnique Energy & Environment Master Programs” that gathers a large number of Alumni, Professors and academic or industrial partners
These links will appear in time on your Polytechnique SynapseS account
Also do not hesitate to contact your professors.
About the procedure:
 Once you will have found an interesting internship, first contact Alexandre STEGNER for his approval of the subject and of the hosting organisation.
 At the end of November you will receive information about internship contract procedure from Mrs Michèle Gesbert, in charge of Master2 internships.
 A “Convention de Stage” will be signed by you, your host organisation, a STEEM academic referent, and Ecole Polytechnique.
STEEM2 internships will start from the end of March and shall last 20 to 24 weeks (5 to 6 months).
A STEEM2 internship must be a research internship.
However, the word research can be appreciated quite widely. It is not necessarily academic research, it may be scientific, technical, industrial or economic research or development, but it is not an execution internship. Indeed, the internship must not consist of carrying out standard works, whether predefined or not, within a department; the internship must have a welldefined objective and must lead to the realization of an original deliverable: a software, an experiment, a study that can be scientific, statistical, economic .... but original!
There is also no restriction on the organization hosting you: academic lab. or company, from startup to large industrial group, or administration or paraadministrative body, in France or abroad (but this may cause visa problems).
Fundamentally what is important is to assess the managerial capacity of the host organization, how it can guide you in your research and what you can learn there.
When choosing your internship, think about what you plan to do the year after. Do you plan to begin a PhD, to find a job in a company, to launch a startup or anything else? There will be many opportunities for you, but some of them require a specific internship.
For an academic PhD prefer an internship in an academic lab, it may give you good references and even propose PhD opportunities. A thesis in a company is also conceivable, in this case favour rather important companies, small ones rarely have the means to support a PhD student.
For a future career in a company remember to become the real specialist they will need, the internship is there to train you in a specialty but also to give you the opportunity to prove your scientific and technical competences, often big or small companies use internships to test their future employers, it will be your last student exam so don’t miss it!
Whatever the type of internship you will choose, your ability to present the progress of your work and your results clearly and synthetically is also very important and may influence strongly your future. Therefore, the internship ends with a report and an oral defence, see on SynapseS the dedicated advices for these topics.
You will have to choose an internship at the end of December or during January, to this end you will benefit on the web of a lot of information:
 Dedicated proposals received for STEEM students will be posted.
 The list of internships done by STEEM, REST and WAPE students during the previous years.
 The Polytechnique Career Center internship proposals whatever the discipline.
 You may join the LINKEDIN group “Ecole Polytechnique Energy & Environment Master Programs” that gathers a large number of Alumni, Professors and academic or industrial partners
These links will appear in time on your Polytechnique SynapseS account
Also do not hesitate to contact your professors.
About the procedure:
 Once you will have found an interesting internship, first contact Alexandre STEGNER for his approval of the subject and of the hosting organisation.
 At the end of November you will receive information about internship contract procedure from Mrs Michèle Gesbert, in charge of Master2 internships.
 A “Convention de Stage” will be signed by you, your host organisation, a STEEM academic referent, and Ecole Polytechnique.
MAP661D  Stochastic Optimization and Management of Energies (20202021)
Master ParisTech REST
Renewable Energy Science and Technology
Graduate Degree STEEM
Energy Environment: Science Technology and Management
MAP661D 20192020
Stochastic and Decentralized Optimization
for the Management of MicroGrids
Michel DE LARA, CERMICSÉcole des Ponts ParisTech
Eligibility/Prerequisites.
 Mathematical skills (meaning the ability to manipulate abstract concepts, and to make calculus). Computer skills (meaning having already programmed).
 Mathematical background: linear algebra (vectors, matrices, symmetric matrices, positive symmetric matrices); topology on (open and closed subsets, bounded subsets, compacity, continuity of functions); differential calculus on (differentiation, partial derivatives, gradient, Jacobian matrix).
 Continuous optimization: linear programming, convexity, Lagrange multipliers and duality, firstorder optimality conditions. [Ber96]
 Probability calculus: probability space, probability, random variables, independence, law of large numbers. [Fel68]
 Software Scicoslab to be installed Scicoslab (else, install software Scilab)
Learning outcomes. After the course the student should be able to
 design mathematical models for energy storage and delivery of renewable energies, especially in microgrids, and formulate costminimization problems,
 use the scientific software Scicoslab and numerically solve small scale problems.
Course main content. The course mixes theoretical sessions, modeling exercises and computer sessions.
In introduction, we present examples of microgrid and virtual power plant management  where the question of electrical storage is put, due to the need to answer a varying demand and to incorporate intermittent and highly variable renewable energies. During the course, we will present concepts and tools to formulate such problems as stochastic dynamic optimization problems. For this purpose, the first sessions are dedicated to mathematical recalls in probability and optimization, followed by an introduction to the scientific software Scicoslab.
Then, we turn to stochastic optimization. In a deterministic optimization problem, the values of all parameters are supposed known. What happens when this is no longer the case? And when some values are revealed during the stages of decision? We present stochastic optimization, at the same time as a frame to formulate problems under uncertainty, and as methods to solve them according to the formulation. More precisely, we present twostage stochastic programming (and the resolution on scenario tree or by scenarios) and multistage stochastic control (and the resolution by stochastic dynamic programming). We finish with the Stochastic Dual Dynamic Programming (SDDP) algorithm (used in commercial software in the world of the energy), which mixes dynamic programming and cutting plane algorithm. Depending on time availability, we will try to shed light on decomposition methods that lead to decentralized optimization (especially adapted to microgrid management).
Modeling exercises and computer sessions tackle issues like optimal economic dispatch of energy production units, storage/delivery optimization problem to buffer an intermittent and variable source of energy, dam optimal management with stochastic water inflows, battery optimal management with renewable energy inputs.
Examination and requirements for final grade. At the end of each computer session, the student produces a report, which receives a mark after evaluation. Miniexams, presence and participation also contribute to the final grade.
Contact person. Michel De Lara (CermicsÉcole des Ponts ParisTech) professional webpage
Link course. http://cermics.enpc.fr/~delara/TEACHING/STEEM2REST/
course webpage
Link master REST. http://www.masterrenewableenergy.com/
master REST webpage
Link Graduate Degree STEEM. https://portail.polytechnique.edu/graduatedegree/steem/
Graduate Degree STEEM map of the courses rooms
Program
1 / September 2019
Admission exam (14h3016h00)
2 / Tuesday 7, January 2020 (Amphi Gregory)
Scanning the course schedule (14h0014h30)
Introductory talk (14h3015h30)
To introduce the course, we present an example of microgrid management that can be solved using stochastic dynamic optimization.
Work done by François Pacaud (Efficacity and CermicsÉcole des Ponts ParisTech)
``Optimal Energy Management of a Urban District'' slides
Lecture and exercises (16h0018h00)
Recalls on probability calculus: probability space, probability, random variables, law of a random variable, mathematical expectation (linearity), indicator function (law, expectation), independence of random variables, almostsure convergence and law of large numbers. [Fel68]
Exercises on probability calculus. The blood testing problem. slides
3 / Tuesday 14, January 2020 (Amphi Gregory)
Lecture and exercises (14h0016h00)
Recalls and exercises on continuous optimization [Ber96]. slides
 Recalls on mathematical background: linear algebra (vectors, matrices, symmetric matrices, positive symmetric matrices); topology on (open and closed subsets, bounded subsets, compacity, continuity of functions); differential calculus on (differentiation, partial derivatives, gradient, Jacobian matrix).
 Recalls on convexity: convex sets, convex functions, strict and strong convexity (characterization by the Hessian in the smooth case), operations preserving convexity.
 Abstract formulation of a minimization problem: criterion, constraints. Sufficient conditions for the existence of a minimum (continuity and compacity/coercivity).
Sufficient condition for the uniqueness of a minimum (strict convexity). Exercises with a quadratic objective function on an interval.
Exercises (16h3018h00)
We present, under the form of an exercise, an example of optimization problem under uncertainty: ``the newsvendor problem''. slides
4 / Tuesday 21, January 2020 (Amphi Gregory)
Computer session
Introduction to the scientific software Scicoslab. [CCN10] computer session
Computer session
The newsvendor problem (only the Section 1, The newsvendor problem (integer formulation))
5 / Tuesday 28, January 2020 (Amphi Gregory)
Modeling session
``Day Ahead Energy Markets'' slides
Computer session
The newsvendor problem (only the Section 1, The newsvendor problem (integer formulation))
You will send the results of the computer project The newsvendor problem (only the Section 1, The newsvendor problem (integer formulation))
under the form of a pdf file TP1_REST_2019_MYNAME.pdf
or TP1_STEEM_2019_MYNAME.pdf
to delara@cermics.enpc.fr before Monday 4 February 2020, 9 AM.
 You can choose any software for the computation (but Scicoslab is recommended).
 You can choose any text editor for the report.
 You can insert computer code, but in limited amount.
 The report will display on the first page: title, given name followed by family name, date, mention of REST 20192020or of STEEM 20192020.
6 / Tuesday 4, February 2020 (Amphi Gregory)
Lecture
Twostage stochastic programming on a scenario tree.
Nonanticipativity constraint along scenarios: tree representation. slides
[SDR09]
Computer session
Sizing of reserves for the balancing on an electric market
(linear and quadratic optimization on a tree)
Exercises
Exercises on probability, optimization and twostage stochastic programming.
7 / Tuesday 11, February 2020 (Amphi Gregory)
Recalls and exercises on continuous optimization [Ber96]. slides
 Definition of a local minimizer; necessary condition in the differentiable case. Formulation of a minimization problem under explicit equality constraints.
Necessary firstorder optimality conditions in the regular/affine equality constraints case; Lagrangian, duality, multipliers.
Sufficient firstorder optimality conditions in the convexaffine case. Exercises.
Computer session
Sizing of reserves for the balancing on an electric market
(linear and quadratic optimization on a tree)
8 / Tuesday 18, February 2020 (Amphi Gregory)
Lecture
Twostage stochastic programming on a fan. slides
Nonanticipativity constraint along scenarios.
Scenario decomposition by Lagrangian relaxation. Progressive Hedging [RW91].
Computer session (16h0018h00)
Sizing of reserves for the balancing on an electric market
(linear and quadratic optimization on a fan)
You will send the results of the computer project Sizing of reserves for the balancing on an electric market
under the form of a pdf file TP2_REST_2019_MYNAME.pdf
or TP2_STEEM_2019_MYNAME.pdf
to delara@cermics.enpc.fr before 20 February 2020, 18h.
9 / Tuesday 3, March 2020 (Amphi Gregory)
Correction of the computer project (14h0014h30)
Exam (14h3016h00)
Exam on optimization and twostage stochastic programming.
Correction of the exam (16h3017h00)
Lecture and exercises
Obtaining the value of a mine by dynamic programming.
Dynamical models of storage (battery models, dam models).
Dynamical sequential systems with control.
10 / Tuesday 10, March 2020 (Amphi Gregory)
Lecture and exercises (14h0017h00)
Dynamical sequential systems with control and noise.
Optimal control of stochastic dynamical sequential systems. slides
Stochastic dynamic programming. Curse of dimensionality. slides
Exercise on stochastic dynamic programming.
Computer session (17h0018h00)
Dam optimal management under uncertainty
11 / Tuesday 17, March 2020 (Amphi Gregory)
Computer session (14h0018h00)
Dam optimal management under uncertainty
You will send a report of the computer project Dam optimal management under uncertainty
(up to Question 8 included) under the form of a pdf file TP3_REST_2019_MYNAME.pdf
or TP3_STEEM_2019_MYNAME.pdf
to delara@cermics.enpc.fr before Wednesday 20 March 2020, 15h.
Bibliography

 Ber96
 D. P. Bertsekas.
Constrained Optimization and Lagrange Multiplier Methods.
Athena Scientific, Belmont, Massachusetts, 1996.  Ber00
 D. P. Bertsekas.
Dynamic Programming and Optimal Control.
Athena Scientific, Belmont, Massachusetts, second edition, 2000.
Volumes 1 and 2.  CCCD15
 P. Carpentier, J.P. Chancelier, G. Cohen, and M. De Lara.
Stochastic MultiStage Optimization. At the Crossroads between Discrete Time Stochastic Control and Stochastic Programming.
SpringerVerlag, Berlin, 2015.  CCN10
 Stephen Campbell, JeanPhilippe Chancelier, and Ramine Nikoukhah.
Modeling and Simulation in Scilab/Scicos with ScicosLab 4.4.
SpringerVerlag, New York, 2 edition, 2010.  Fel68
 W. Feller.
An Introduction to Probability Theory and its Applications, volume 1.
Wiley, New York, third edition, 1968.  RW91
 R.T. Rockafellar and R. JB. Wets.
Scenarios and policy aggregation in optimization under uncertainty.
Mathematics of operations research, 16(1):119147, 1991.  SDR09
 A. Shapiro, D. Dentcheva, and A. Ruszczynski.
Lectures on stochastic programming: modeling and theory.
The society for industrial and applied mathematics and the mathematical programming society, Philadelphia, USA, 2009.
Master ParisTech REST
Renewable Energy Science and Technology
Graduate Degree STEEM
Energy Environment: Science Technology and Management
MAP661D 20192020
Stochastic and Decentralized Optimization
for the Management of MicroGrids
Michel DE LARA, CERMICSÉcole des Ponts ParisTech
Eligibility/Prerequisites.
 Mathematical skills (meaning the ability to manipulate abstract concepts, and to make calculus). Computer skills (meaning having already programmed).
 Mathematical background: linear algebra (vectors, matrices, symmetric matrices, positive symmetric matrices); topology on (open and closed subsets, bounded subsets, compacity, continuity of functions); differential calculus on (differentiation, partial derivatives, gradient, Jacobian matrix).
 Continuous optimization: linear programming, convexity, Lagrange multipliers and duality, firstorder optimality conditions. [Ber96]
 Probability calculus: probability space, probability, random variables, independence, law of large numbers. [Fel68]
 Software Scicoslab to be installed Scicoslab (else, install software Scilab)
Learning outcomes. After the course the student should be able to
 design mathematical models for energy storage and delivery of renewable energies, especially in microgrids, and formulate costminimization problems,
 use the scientific software Scicoslab and numerically solve small scale problems.
Course main content. The course mixes theoretical sessions, modeling exercises and computer sessions.
In introduction, we present examples of microgrid and virtual power plant management  where the question of electrical storage is put, due to the need to answer a varying demand and to incorporate intermittent and highly variable renewable energies. During the course, we will present concepts and tools to formulate such problems as stochastic dynamic optimization problems. For this purpose, the first sessions are dedicated to mathematical recalls in probability and optimization, followed by an introduction to the scientific software Scicoslab.
Then, we turn to stochastic optimization. In a deterministic optimization problem, the values of all parameters are supposed known. What happens when this is no longer the case? And when some values are revealed during the stages of decision? We present stochastic optimization, at the same time as a frame to formulate problems under uncertainty, and as methods to solve them according to the formulation. More precisely, we present twostage stochastic programming (and the resolution on scenario tree or by scenarios) and multistage stochastic control (and the resolution by stochastic dynamic programming). We finish with the Stochastic Dual Dynamic Programming (SDDP) algorithm (used in commercial software in the world of the energy), which mixes dynamic programming and cutting plane algorithm. Depending on time availability, we will try to shed light on decomposition methods that lead to decentralized optimization (especially adapted to microgrid management).
Modeling exercises and computer sessions tackle issues like optimal economic dispatch of energy production units, storage/delivery optimization problem to buffer an intermittent and variable source of energy, dam optimal management with stochastic water inflows, battery optimal management with renewable energy inputs.
Examination and requirements for final grade. At the end of each computer session, the student produces a report, which receives a mark after evaluation. Miniexams, presence and participation also contribute to the final grade.
Contact person. Michel De Lara (CermicsÉcole des Ponts ParisTech) professional webpage
Link course. http://cermics.enpc.fr/~delara/TEACHING/STEEM2REST/
course webpage
Link master REST. http://www.masterrenewableenergy.com/
master REST webpage
Link Graduate Degree STEEM. https://portail.polytechnique.edu/graduatedegree/steem/
Graduate Degree STEEM map of the courses rooms
Program
1 / September 2019
Admission exam (14h3016h00)
2 / Tuesday 7, January 2020 (Amphi Gregory)
Scanning the course schedule (14h0014h30)
Introductory talk (14h3015h30)
To introduce the course, we present an example of microgrid management that can be solved using stochastic dynamic optimization.
Work done by François Pacaud (Efficacity and CermicsÉcole des Ponts ParisTech)
``Optimal Energy Management of a Urban District'' slides
Lecture and exercises (16h0018h00)
Recalls on probability calculus: probability space, probability, random variables, law of a random variable, mathematical expectation (linearity), indicator function (law, expectation), independence of random variables, almostsure convergence and law of large numbers. [Fel68]
Exercises on probability calculus. The blood testing problem. slides
3 / Tuesday 14, January 2020 (Amphi Gregory)
Lecture and exercises (14h0016h00)
Recalls and exercises on continuous optimization [Ber96]. slides
 Recalls on mathematical background: linear algebra (vectors, matrices, symmetric matrices, positive symmetric matrices); topology on (open and closed subsets, bounded subsets, compacity, continuity of functions); differential calculus on (differentiation, partial derivatives, gradient, Jacobian matrix).
 Recalls on convexity: convex sets, convex functions, strict and strong convexity (characterization by the Hessian in the smooth case), operations preserving convexity.
 Abstract formulation of a minimization problem: criterion, constraints. Sufficient conditions for the existence of a minimum (continuity and compacity/coercivity).
Sufficient condition for the uniqueness of a minimum (strict convexity). Exercises with a quadratic objective function on an interval.
Exercises (16h3018h00)
We present, under the form of an exercise, an example of optimization problem under uncertainty: ``the newsvendor problem''. slides
4 / Tuesday 21, January 2020 (Amphi Gregory)
Computer session
Introduction to the scientific software Scicoslab. [CCN10] computer session
Computer session
The newsvendor problem (only the Section 1, The newsvendor problem (integer formulation))
5 / Tuesday 28, January 2020 (Amphi Gregory)
Modeling session
``Day Ahead Energy Markets'' slides
Computer session
The newsvendor problem (only the Section 1, The newsvendor problem (integer formulation))
You will send the results of the computer project The newsvendor problem (only the Section 1, The newsvendor problem (integer formulation))
under the form of a pdf file TP1_REST_2019_MYNAME.pdf
or TP1_STEEM_2019_MYNAME.pdf
to delara@cermics.enpc.fr before Monday 4 February 2020, 9 AM.
 You can choose any software for the computation (but Scicoslab is recommended).
 You can choose any text editor for the report.
 You can insert computer code, but in limited amount.
 The report will display on the first page: title, given name followed by family name, date, mention of REST 20192020or of STEEM 20192020.
6 / Tuesday 4, February 2020 (Amphi Gregory)
Lecture
Twostage stochastic programming on a scenario tree.
Nonanticipativity constraint along scenarios: tree representation. slides
[SDR09]
Computer session
Sizing of reserves for the balancing on an electric market
(linear and quadratic optimization on a tree)
Exercises
Exercises on probability, optimization and twostage stochastic programming.
7 / Tuesday 11, February 2020 (Amphi Gregory)
Recalls and exercises on continuous optimization [Ber96]. slides
 Definition of a local minimizer; necessary condition in the differentiable case. Formulation of a minimization problem under explicit equality constraints.
Necessary firstorder optimality conditions in the regular/affine equality constraints case; Lagrangian, duality, multipliers.
Sufficient firstorder optimality conditions in the convexaffine case. Exercises.
Computer session
Sizing of reserves for the balancing on an electric market
(linear and quadratic optimization on a tree)
8 / Tuesday 18, February 2020 (Amphi Gregory)
Lecture
Twostage stochastic programming on a fan. slides
Nonanticipativity constraint along scenarios.
Scenario decomposition by Lagrangian relaxation. Progressive Hedging [RW91].
Computer session (16h0018h00)
Sizing of reserves for the balancing on an electric market
(linear and quadratic optimization on a fan)
You will send the results of the computer project Sizing of reserves for the balancing on an electric market
under the form of a pdf file TP2_REST_2019_MYNAME.pdf
or TP2_STEEM_2019_MYNAME.pdf
to delara@cermics.enpc.fr before 20 February 2020, 18h.
9 / Tuesday 3, March 2020 (Amphi Gregory)
Correction of the computer project (14h0014h30)
Exam (14h3016h00)
Exam on optimization and twostage stochastic programming.
Correction of the exam (16h3017h00)
Lecture and exercises
Obtaining the value of a mine by dynamic programming.
Dynamical models of storage (battery models, dam models).
Dynamical sequential systems with control.
10 / Tuesday 10, March 2020 (Amphi Gregory)
Lecture and exercises (14h0017h00)
Dynamical sequential systems with control and noise.
Optimal control of stochastic dynamical sequential systems. slides
Stochastic dynamic programming. Curse of dimensionality. slides
Exercise on stochastic dynamic programming.
Computer session (17h0018h00)
Dam optimal management under uncertainty
11 / Tuesday 17, March 2020 (Amphi Gregory)
Computer session (14h0018h00)
Dam optimal management under uncertainty
You will send a report of the computer project Dam optimal management under uncertainty
(up to Question 8 included) under the form of a pdf file TP3_REST_2019_MYNAME.pdf
or TP3_STEEM_2019_MYNAME.pdf
to delara@cermics.enpc.fr before Wednesday 20 March 2020, 15h.
Bibliography

 Ber96
 D. P. Bertsekas.
Constrained Optimization and Lagrange Multiplier Methods.
Athena Scientific, Belmont, Massachusetts, 1996.  Ber00
 D. P. Bertsekas.
Dynamic Programming and Optimal Control.
Athena Scientific, Belmont, Massachusetts, second edition, 2000.
Volumes 1 and 2.  CCCD15
 P. Carpentier, J.P. Chancelier, G. Cohen, and M. De Lara.
Stochastic MultiStage Optimization. At the Crossroads between Discrete Time Stochastic Control and Stochastic Programming.
SpringerVerlag, Berlin, 2015.  CCN10
 Stephen Campbell, JeanPhilippe Chancelier, and Ramine Nikoukhah.
Modeling and Simulation in Scilab/Scicos with ScicosLab 4.4.
SpringerVerlag, New York, 2 edition, 2010.  Fel68
 W. Feller.
An Introduction to Probability Theory and its Applications, volume 1.
Wiley, New York, third edition, 1968.  RW91
 R.T. Rockafellar and R. JB. Wets.
Scenarios and policy aggregation in optimization under uncertainty.
Mathematics of operations research, 16(1):119147, 1991.  SDR09
 A. Shapiro, D. Dentcheva, and A. Ruszczynski.
Lectures on stochastic programming: modeling and theory.
The society for industrial and applied mathematics and the mathematical programming society, Philadelphia, USA, 2009.