MA413E - Combinatorial optimization

Objectives

General objective:

Upon completion of this course the student will be able to:
- identify an optimization problem in a real-world context,
- formulate some simple continuous or combinatorial optimization problems in an appropriate modeling framework
- describe and apply manually a set of basic mathematical and graph optimization algorithms
- choose and apply an appropriate algorithm to solve basic optimization problems

Detailed objectives:

Upon completion of this course the student will be able to:
- identify and differentiate continuous and combinatorial optimization problems as well as linear and non-linear optimization problems,
- describe and model basic problems of graph theory : minimum weight spanning tree problem, shortest path problem, project scheduling problem, maximum flow problem,
- build linear/ non-linear mathematical optimization models
- describe and apply manually the following concepts and algorithms:
- optimality conditions,
- gradient methods,
- projected gradient methods,
- penalty methods,
- Simplex algorithm,
- branch and bound search,
- basic algorithms of graph theory : Prim, Kruskal, Dijkstra, Bellman and Ford-Fulkerson