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
- 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
(else, install software Scilab)
- Free software Scicoslab auto-training
to be able to do the Monday computer session.
Campus Casa Central, UTFSM
Two-stage Stochastic Programming
- 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
Sizing of reserves for the balancing on an electric market
Stochastic Dynamic Programming
- Examples of micro-grid management problems: metro station, domestic
- 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
- Examples and mathematical background
- About decomposition in stochastic optimization
- Dual approximate dynamic programming (DADP)
- Hydro valleys management problem