Operational Research [ LINMA2491 ]

> https://icampus.uclouvain.be/claroline/course/index.php?cid=LINMA2491

LINMA1702 (Optimisation methods and models I)

• Mathematical background (duality, KKT optimality conditions, monotone operators)
• Mathematical programming models and languages
• Applications: finance, logistics, risk management, energy

In reference to the AA standard, this course contributes to the development, acquisition and evaluation of the following learning outcomes:

• AA1.1, AA1.2, AA1.3
• AA2.2, AA2.5

More specifically, at the end of the course students will be able to:

• Use mathematical programming models in order to formulate decision-making problems under uncertainty and develop algorithms for solving these models

Acquired learning:

• Implement decomposition algorithms for solving large-scale optimization problems in two mathematical programming languages: AMPL and/or Mosel
• Identify and implement the most appropriate solution algorithms for specific classes of optimization problems under uncertainty that arise in finance, energy and logistics

• Written or oral exam, depending on the size of the class
• Course project and/or homework assignments (to be determined)

2 hours of magistral courses per week, and 2 hours of training sections per week. Homeworks and term projects will be evaluated by the instructor and/or the teaching assistant.

• Stochastic programming models
• Value of perfect information and the value of the stochastic solution
• The L-shaped method in two and multiple stages
• Multi-cut L-shaped algorithm
• Stochastic dual dynamic programming
• Scenario selection and importance sampling
• Lagrangian relaxation
• Stochastic integer programming
• Monotone operators, proximal point algorithms and progressive hedging

• Course notes
• Printouts from textbooks or archived journals will be provided during lectures. The following textbook will be followed closely for most of the course: John Birge, Francois Louveaux, "Introduction to Stochastic Programming"