Optimization
A.Y. 2024/2025
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.
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.
Lesson period: First trimester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
First trimester
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
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).
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.
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:
Thursday 1.00 - 4.00 pm. Send me an email to schedule a meeting
room 33 III floor and Teams