Optimization

A.Y. 2020/2021
6
Max ECTS
40
Overall hours
SSD
SECS-S/06
Language
English
Learning objectives
This course aims to introduce students to optimization methods in a static context. The instruments,
explained during the course, are crucial to describe the efficient behaviour of economic agents.
Both unconstrained and constrained optimization methods will be presented during the course.
At the end of the course students should be able to represent the behaviour of agents
through the formalization of a constrained optimization problem and solve it using the mathematical
results and the graphical approaches discussed during classes.
Expected learning outcomes
At the end of the course, the student will know the basic elements of the optimization theory in a static framework; will be able to formulate appropriate optimization problems; will possess an adequate mathematical terminology; will learn the main theoretical results and practical methods related to the optimization problems that can describe the behaviour of an economic agent.
Course syllabus and organization

Single session

Responsible
Lesson period
First trimester
All information will be posted on the course webpage on http://ariel.unimi.it.

Lectures will take place in presence. In case of a new directive from the University due to a
worsening of the situation, Lectures will take place online in synchronous way on the Zoom (or MSTeams) platform according to the timetable provided by the University. Lectures will possibly be recorded and made available to the students to be followed in an asynchronous way.

The program of the course will not change.

The written exams during the emergency will maintain the same structure of the usual ones.
Course syllabus
1. Multivariate Calculus
1.a Domain and Level curve
1.b Partial Derivatives
1.c Concave and Convex Functions
1.d Implicit Functions
1.e Differentiability
2. Static Optimization
2.a First and Second Order Conditions for Unconstrained Problems
2.b Constrained Optimization Problems: Equality Constraints
First and Second Order Conditions
2.c Constrained Optimization Problems: Inequality Constraints
First and Second Order Conditions
2.d Constrained Optimization Problems: Nonnegativity Constraints
First and Second Order Conditions
Prerequisites for admission
Calculus I and Linear Algebra.
Teaching methods
Lecture and tutorial
Teaching Resources
Knut Sydsaeter, Peter Hammond, Atle Seierstad, Arne Strom, Essential Mathematics for Economic Analysis, Financial Times (Chapters 11, 12, 13, 14, 17)

Knut Sydsaeter, Peter Hammond, Atle Seierstad, Arne Strom, Further Mathematics for Economic Analysis, Financial Times Prentice Hall, 2008 (chapters 1,2,3).
Assessment methods and Criteria
Written exam composed of practical exercises
where the students have to choose the best method among those
discussed in classes and apply them in a correct way.
SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES - University credits: 6
Lessons: 40 hours
Professor: Mercuri Lorenzo
Educational website(s)
Professor(s)
Reception:
Tuesday from 2.30 p.m. to 5.30 p.m.
Microsoft office Teams (https://work.unimi.it/servizi/servizi_tec/1536.htm)