AIMS AND CONTENT

AIMS AND LEARNING OUTCOMES

The aim of the course is to introduce the basic principles and methods of resolution for optimization problems. Different classes of optimization problems will be considered: (1) unconstrained optimization, (2) constrained optimization, (3) convex optimization, (4) linear programming, (5) quadratic optimization problems, (6) nonlinear problems, (7) mixed-integer programming. Then, the resolution methods will be introduced and the a specific software tool able to solve optimization problems will be described. Once the course is completed, students will be able to recognize the class of an optimization problem and to identify and implement its resolution.

TEACHING METHODS

Classroom lectures with discussion of application problems and implementation in different software environments (matlab/GAMS).

SYLLABUS/CONTENT

1. Unconstrained optimization
2. Constrained optimization:
   • First order optimality conditions
   • Second order optimality conditions
3. Convex optimization problems
4. Active Set Methods:
   • Projected Gradient Method
5. Classification of optimization problems:
   • Linear programming
   • Quadratic programming
   • Non-linear problems (outline)
   • Mixed-integer optimization (outline)
6. MATLAB/GAMS implementation of optimization problems

RECOMMENDED READING/BIBLIOGRAPHY

• J. Nocedal, S. J. Wright, “Numerical Optimization”, Springer, 1999
• Matlab-Manual: https://it.mathworks.com/help/
• GAMS-Manual: User's Guide (gams.com)

TEACHERS AND EXAM BOARD

Exam Board

MARIO NERVI (President)

MASSIMO BRIGNONE

FABIO D'AGOSTINO

PAOLA GIRDINIO

DANIELE MESTRINER

PAOLO MOLFINO

GIORGIO MOLINARI

GABRIELE MOSAICO

MANSUETO ROSSI

MATTEO SAVIOZZI (President Substitute)

EUGENIA TORELLO (President Substitute)

LESSONS

LESSONS START

https://corsi.unige.it/8731/p/studenti-orario

EXAMS

EXAM DESCRIPTION

Oral exam with Software exercises.

Exam schedule