The first part of the course deals with modeling for stochastic optimization:
1) Risk measures: static measures (polyhedrons, spectral, distortion), dynamic;
2) Two-stage and multi-stage models without risk aversion:
a) Examples of two-stage and multi-stage problems: problem of the newspaper seller; a production management problem; a problem of portfolio management.
b) Two-stage linear problems.
c) Problems with two general stages.
d) Multi-stage formulation.
3) Two-stage and multi-stage models with risk aversion.
The second part is about optimization algorithms:
1) Stochastic gradient algorithm.
2) Stochastic mirror descent algorithm.
3) Dantzig-Wolfe decomposition.
4) Cutting plan method.
5) SDDP, AND, DOASA.
· A. Shapiro, D. Dentcheva, A. Ruszczynski, Lectures on Stochastic Programming: Modeling and Theory, SIAM, Philadelphia, 2009.
· S. Boyd, L. Vandenberghe, Convex Optimization, Cambridge University Press, 2009.
· J.R. Birge, F. Louveaux, Introduction to Stochastic Programming, Springer, 1997.
· M.V.F. Pereira, L.M.V.G Pinto, Multi-stage stochastic optimization applied to energy planning, Mathematical Programming, 52, 359-375, 1991.
· R.T Rockafellar, S. Uryasev, Optimization of Conditional Value-at-Risk, The journal of Risk, 2, 21-41, 2000.
· V. Guigues, Multistep stochastic mirror descent for risk-averse convex stochastic programs based on extended polyhedral risk measures, Mathematical Programming, 163, 169-212, 2017.
· V. Guigues, R. Henrion, Joint dynamic probabilistic constraints with projected linear decision rules, Optimization Methods & Software, 32 (5), 1006-1032, 2017.
Convergence Analysis of Sampling-Based Decomposition Methods for Risk-Averse Multistage Stochastic Convex Programs, Siam Journal on Optimization, 26, 2468-2494, 2016.