Mini-Course -- 13-14 March 2017

Stochastic and Dynamic Optimization.

Optimal Energy Storage and Allocation.

**Michel DE LARA, CERMICS-École des Ponts ParisTech**

*Eligibility/Pre-requisites.*

- Mathematical skills. Computer skills.
- Probability calculus: probability space, probability, random variables, law of a random variable, indicator function, mathematical expectation, independence of random variables, almost-sure convergence and law of large numbers.
- Continuous optimization
- Convexity: convex sets, convex functions, strict and strong convexity (characterization by the Hessian in the smooth case), operations preserving convexity
- Free software Scicoslab to be installed
`Scicoslab`(else, install software Scilab) - Free software Scicoslab auto-training
`computer session`to be able to do the Monday computer session.

*Room.*

Campus Casa Central, UTFSM
`map`

*Link course.*
` http://cermics.enpc.fr/~delara/TEACHING/AC3E_2017/`

`course webpage`

Auditorio B-2.38 (Michel De Lara)

Two-stage Stochastic Programming slides

- The newsvendor problem, without and with backorder; worst case vs. expectation risk criteria
- Two stage stochastic programming (linear case); initial and recourse decision variables; formulation on a tree
- Two stage stochastic programming (strongly convex case); scenario decomposition algorithm
- Two stage stochastic programming (linear case); Progressive Hedging algorithm

Sala P-306 (Pierre Carpentier, Michel De Lara, François Pacaud, Tristan Rigaut)

`Sizing of reserves for the balancing on an electric market`

Sala P-407 (François Pacaud, Tristan Rigaut)

Stochastic Dynamic Programming
`slides`
`slides`

- Examples of micro-grid management problems: metro station, domestic district, aggregator slides slides
- Examples of stock management problems; notion of discrete-time controlled dynamical systems with noise
- Stochastic optimal control problem formulation; resolution by dynamic programming when noise are white
- Curse of dimensionality, complexity

Sala P-407 (Pierre Carpentier)

- Examples and mathematical background
- About decomposition in stochastic optimization
- Dual approximate dynamic programming (DADP)
- Hydro valleys management problem