Stochastic Optimization

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.

Basic Information

Workload
45 hours
Requirements
Optimization

Mandatory: 

  • 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.

Complementary: 

  • 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.