Learning outcomes of the course unit
At the end of the teaching period the student should be able to deeal with decision problems through the mathematical programmin tools. In particular, the student should build the mathematical model, individuate the appropriate algorithm (possible applying it through the proposed modeling language), and finally derive and interpret the solution of the model.
Basic notions of linear algebra and calculus
Course contents summary
Introduction to Mathematical Programming. Mathematical models. Linear programming: theory and algorithms. Integer linear programming: theory and algorithms.
Nonlinear programming: theory and algorithms. Modeling language AMPL.
In the first part of the course mathematical programming problems are introduced and basic concepts for the definition of mathematical programming problems, representing real decision problems, are illustrated. The modeling language AMPL is also introduced as a powerful tool for a simple use of the most widely employed solvers.
In the second part Linear Programming (LP) problems are introduced. After the discussion of some theoretical issues, the theory itself is employed for the definition of an algorithmic approach (the simplex algorithm). Duality and sensitivity analysys (e.g., the sensitivity of optimal values and solutions to perturbation of the data) are also discussed.
In the third part, Integer Linear Programming (ILP) is introduced. Also here we start with some theoretical issues and then we move to the definition of algorithmic approaches, i.e., cutting plane approaches, branch-and-bound approaches and, for problems with a special structure, dynamic programming approaches.
In the fourth and last part of the course we deal with Nonlinear Programming problems. We discuss the theoretical issue of optimality conditions and present the basic components of the main algorithmic approaches.
Teaching material proposed by the teacher.
Theoretical lessons followed by exercises.
Assessment methods and criteria
Written exam with some questions about the theory (oral optional). Project to be developed at home.
The teaching material is available at the web site lea.unipr.it