Insegnamento a.a. 2019-2020

20603 - OPTIMIZATION

Department of Decision Sciences

Course taught in English
Go to class group/s: 31
DSBA (8 credits - II sem. - OP  |  SECS-S/06)
Course Director:
FILIPPO GAZZOLA

Classes: 31 (II sem.)
Instructors:
Class 31: FILIPPO GAZZOLA


Suggested background knowledge

To feel comfortable in this course you should have attended at least two calculus classes covering the basic concepts of function, derivative, multivariable functions, partial derivatives, finite dimensional optimization, Lagrange multipliers, integrals as well as having a working knowledge of linear algebra (vectors/matrices/eigenvalues/systems).

Mission & Content Summary

MISSION

Mathematics is the language in which most of modern economics is written. The course aims to provide the basic mathematical tools that students need to complete their Economics studies. Moreover, the course develops the analytical thinking skills that students need later on in their academic career.

CONTENT SUMMARY

  • Basics on differential equations, separation of variables, linear equations, linear systems. Partial differentiation, free and constrained optimization, gradient methods.

  • Vector spaces, Banach spaces, Hilbert spaces. Separable spaces, Fourier series: $ell^2$ and $L^2_T$.

  • Continuity, convexity, compactness. Fréchet-derivatives. Fixed points, contractions.

  • Classical problems in calculus of variations, critical points. Maxima and minima, necessary/sufficient conditions. Convexity.
    Control theory, bang-bang principle. Hamiltonians, the Pontryagin maximum principle.

  • Dynamic programming. The Hamilton-Jacobi-Bellman equation.


Intended Learning Outcomes (ILO)

KNOWLEDGE AND UNDERSTANDING

At the end of the course student will be able to...
  • Carry out a formal mathematical proof.
  • Recognize the abstract mathematical structures that underline modern theories.
  • Master vector spaces techniques.
  • Solve optimization problems from calculus of variations.
  • Set up and solve control theory problems.
  • Solve dynamic optimization problems.

APPLYING KNOWLEDGE AND UNDERSTANDING

At the end of the course student will be able to...
  • Apply to economics and to the social sciences the techniques of contemporary mathematics.
  • Work out both the quantitative and the qualitative perspectives.
  • Solve dynamic optimization problems which are key in Economic Theory.
  • Master topological arguments which are important in Game Theory and Microeconomics.

Teaching methods

  • Face-to-face lectures
  • Exercises (exercises, database, software etc.)

DETAILS

Every one/two weeks there is a problem session where mathematical problems concerning the topics taught in class are discussed and solved.


Assessment methods

  Continuous assessment Partial exams General exam
  • Written individual exam (traditional/online)
     x

ATTENDING AND NOT ATTENDING STUDENTS

Written exam.


Teaching materials


ATTENDING AND NOT ATTENDING STUDENTS

Lecture notes.

Last change 05/06/2019 22:30