Mathematics (2021/2022)

Course code
4S003790
Name of lecturers
Alberto Peretti, Letizia Pellegrini
Coordinator
Alberto Peretti
Number of ECTS credits allocated
7.5
Academic sector
SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES
Language of instruction
English
Location
VERONA
Period
A.A. 21/22 dottorato dal Oct 1, 2021 al Sep 30, 2022.

Lesson timetable

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Learning outcomes

The aim of the course is to recall some notions of linear algebra, introduce some basic concepts of calculus for several variables and develop the most important topics on unconstrained and constrained optimization.

Syllabus

Linear algebra: matrix algebra, determinants, rank, quadratic forms, sign of a quadratic form and definite matrices.
Calculus: functions of several variables, level sets, differential calculus for functions of several variables, convex functions.
Unconstrained optimization: first order optimality conditions, second order optimality conditions.
Constrained Optimization: the Weierstrass Theorem. Constrained optimization with equality constraints, Lagrange theorem. Lagrangian function and optimality conditions. Constrained optimization with inequality constraints, Kuhn-Tucker theorem. Convex problems.

Reference books

Vedi la bibliografia dell'insegnamento

Assessment methods and criteria

Written exam. Intermediate tests are proposed during the course.