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First Semester 
Teaching style
Lingua Insegnamento

Informazioni aggiuntive

Course Curriculum CFU Length(h)
[60/65]  MATHEMATICS [65/20 - Ord. 2012]  Applicativo 6 48


The course has as main objectives those of: (i) providing students with the tools for knowledge and the ability to understand constrained and unconstrained non-linear optimization, (ii) providing students with the software tools for non-linear optimization, (iii) teaching how to implement a numerical algorithm for non-linear optimization and to prove the convergence theorem thereof.

In particular, according to the Dublin Descriptors
- Knowledge and understanding: provide students with the tools to develop original ideas derived from the knowledge acquired and the ability to understand.
- applying knowledge and understanding: provide students with the tools to mathematically formalize problems coming from the real world.
- making judgments: provide students with the tools for critical analysis of the problem to be analyzed.
- Communication skills: providing students with the tools to communicate the knowledge elaborated and applied in different contexts.
- Learning skills: provide students with the tools to study independently managing the time spent studying.


Basic knowledge of mathematical analysis and algebra, geometry, theory and study of data structures (useful).


Convex analysis: convex functions and convex sets. Non-Linear optimization models.

Optimality conditions: feasible directions and descent directions, optimal conditions for unconstrained and constrained problems, Karush-Kuhn-Tucker conditions, quadratic programming.

Unconstrained optimization: line search algorithms, gradient method. Newton's method, method of conjugate directions, Quasi-Newton methods.

Constrained optimization:: penalty methods, augmented Lagrangian method, barrier methods and interior-point methods.

Decomposition techniques: Lagranziano relaxation, column generation methods, Bender decomposition.

The course includes the use of software tools to solve non-linear programs along with the implementation of numerical algorithms.

Teaching Methods

The course consists of 48 hours of lectures of which 30 are devoted to lectures and 18 to resume foundamental concepts. During these appropriate calculation tools are provided and how to use them. During lectures, the computer is used to implement numerical algorithms or optimization softwares. Group tests will be organized during the class.

Verification of learning

The evaluation is performed with both a written and oral examination. The evaluation is performed on the basis of the following criteria:
- clarity and correctness of the written examination’s solution;
- ability to identify the topic of the question during the oral examination and to learn to highlight the fundamental theoretical and applied aspects.
The first criterion allows to
- verify the ability to apply modeling and algorithmic methodologies
- verify the ability to use the software tools illustrated during the tutorials
The second criterion allows to
- verify the level of acquisition of the knowledge of the subject;
- verify the ability to illustrate and argue the methodologies justifying the theoretical statements;
- verify the learning ability in the single study.

The process of quantification of the evaluation of the test takes place with the contribution of all the aspects and criteria mentioned and can not be coded in a formula or in tables.


1. J. Nocedal, S. Wright. Numerical Optimization. Springer.
2. Lecture notes.

More Information

Notes taken during lessons and tutorials are an useful support to the study process.

Questionnaire and social

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