Universidad Técnica Federico Santa María (UTFSM), Valparaíso, Chile

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

Program

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

$\fbox{Bring your personal laptop with free software Scicoslab installed.}$
$\fbox{You are supposed to practice the free software Scicoslab}$

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

Advanced decomposition methods in stochastic optimal control slides