Optimization fundamentals

Goal : To provide the fundamental concepts and tools related to operational research and game theory which will be applied to different transport domains. Important issues such incentivation and rewarding play a key role in biasing user behaviour aiming at optimizing system operation.

List of subjects to be presented to the students :

● Optimization models: Objective function, variables and constraints.
● The linear programming model: Convex sets and linear programming algorithms.
● The simplex algorithm
- Duality / Sensitivity Analysis
● Convex functions.
● Optimality criteria: Kuhn-Tucker conditions.
● Quadratic programming.
● Geometric programming.
● Integer programming and algorithms.
● Dynamic programming.
● The transport problem (model).
● Heuristic optimization techniques.