M2 Optimization
	``Stochastic Optimization''

Professors

Pierre Carpentier and Vincent Leclère

The course was given for several years in the M2 Optimization as an introductory course to stochastic optimization.

Goals

The course presents both theoretical and numerical aspects of decision problems with uncertainty, where one sets a probabilistic framework in order to minimize the expectation of a cost. Two directions are explored:

• we investigate the so-called "open-loop" situation, that is, the case where decisions do not depend on information available for the problem, and we thoroughly study the stochastic gradient method and its variants,
• we also study "closed-loop" optimization problems, that is, the case where decisions are based on partial information (often corresponding to measurements made in the past when facing an unknown future).

Structure

• Lesson 1
  • Issues in decision making under uncertainty (P. Carpentier). Slides
  • Convex analysis and probability tools for stochastic optimization - Part I (V. Leclère). Slides


• Lesson 2
  • Stochastic gradient method overview (P. Carpentier). Slides
  • Convex analysis and probability tools for stochastic optimization - Part II (V. Leclère). Slides


• Lesson 3
  • Generalized stochastic gradient method (P. Carpentier). Slides
  • Stochastic Programming. The two-stage case (V. Leclère). Slides


• Lesson 4
  • Bellman operators and Stochastic Dynamic Programming (V. Leclère). Slides
  • Applications of the stochastic gradient method (P. Carpentier). Slides


• Lesson 5
  • Discretization issues of general stochastic optimization problems (P. Carpentier). Slides
  • Scenario decomposition: L-Shaped and Progressive Hedging methods (V. Leclère). Slides


• Lesson 6
  • The Stochastic Dual Dynamic Programming (SDDP) approach (V. Leclère). Slides
  • Decomposition approaches for large scale stochastic optimization problems (P. Carpentier). Slides


• Evaluation
  • Articles presentation (P. Carpentier).
  • Written exam (V. Leclère).

Course resources

• Lecture notes on the stochastic gradient by P. Carpentier (in French)


• Lecture notes on the Auxiliary Problem Principle by P. Carpentier(in French)


• Some chapters of the book "Stochastic Multistage Optimization"
  • Chapter 1 - Issues and Problems in Decision Making under Uncertainty
  • Chapter 2 - Open-Loop Control: the Stochastic Gradient Method
  • Chapter 6 - Discretization Methodology for Stochastic Problems
  • Appendix B - Basics in Probability
  • References


• V. Leclère web page

External resources

• F. Bonnans web page