OPTIMIZATION

The course aims at presenting the basic concepts and methods of optimization. The course provides students with the analytic tools to model and to foresee situations in which a single decision-maker has to find the best choice. The attention focuses on applications in economics, engineering, and computer science. At the end of the course, the students will be able to formulate mathematically a real-life problem, solve numerically the problems using the AMPL code, and realize what the optimal choice is.

The goals of the course are:

1. to acquire base knowledge that allows students to study optimization problems and model techiniques of the decision-making problems. The students will be able to use algorithms for both linear and nonlinear programming problems.
2. to identify and model real-life decision-making problems. In addition, through real examples, the student will be able to implement in AMPL correct solutions for complex problems.
3. to choose and solve autonomously complex decision-making problems and to interpret the solutions.
4. to acquire base communication and reading skills using technical language.
5. to provides students with theoretical and practical methodologies and skills to deal with optimization problems, ranging from computer science to engineering.

For this course, there will be 2 hours of teaching per lecture twice a week. There will be both classroom lessons and laboratory lessons. For each topic, exercises will be solved by the teacher or proposed to students.

A midterm examination will be proposed via a 2-hour written paper. It corresponds to half-part of the program (3CFU). It should be noted that this exam is not compulsory.

1. LINEAR PROGRAMMING

Primal simplex method. Duality and dual simplex method.

2. IINTEGER PROGRAMMING

Branch and Bound method and cutting plane methods in integer programming; KP problem; TSP problem.

3. NONLINEAR PROGRAMMING

Optimality conditions for nonlinear problems; numerical methods for constrained and not constrained problems.

4. SOFTWARE FOR OPTIMIZATION PROBLEMS

GeoGebra, Excel, AMPL, Mathematica.

1. F.S. Hillier, G.J. Lieberman, Introduction to Operations Research, Mc Graw Hill.
2. O.L. Mangasarian, Nonlinear Programming, SIAM Classics in Applied Mathematics.
3. D.P. Bertsekas, Convex Analysis and Optimization, Athena Scientific.
4. D.P. Bertsekas, Nonlinear Programming, Athena Scientific.

Other teaching material will be available on the platform Studium.