Optimization

A.A. 2015/2016
Insegnamento per
6
Crediti massimi
60
Ore totali
Lingua
Inglese
Obiettivi formativi
Students will learn advanced optimization methods and how to use them to model and solve problems in economics and social sciences.

Struttura insegnamento e programma

Edizione attiva
Responsabile
Esercitazioni: 40 ore
Lezioni: 20 ore
Docente: La Torre Davide
Programma
Topics in linear algebra. Review of basic linear algebra. Linear independence. The rank of a matrix. Main results on linear systems. Eigenvalues. Diagonalization. Quadratic forms. Quadratic forms with linear constraints. Partitioned matrices and their inverses.
Linear programming. A simple maximization problem. Graphical solution procedure. Extreme points and the optimal solution. Special cases. General linear programming notation. Sensitivity analysis and interpretation of solution.
Multivariable calculus. Gradients and directional derivatives. Convex sets. Concave and convex functions. Quasiconcave and quasiconvex functions. Taylor's formula. Implicit and inverse function theorems. Degrees of freedom and functional dependence. Differentiability. Existence and uniqueness of solutions of systems of equations.
Static optimization. Extreme points. Local extreme points. Equality constraints: the Lagrange problem. Local second-order conditions. Inequality constraints: nonlinear programming. Sufficient conditions. Comparative statics. Nonnegativity constraints. Concave programming. Precise comparative statics results. Existence of Lagrange multipliers.
Multicriteria decisions. Goal programming: formulation and graphical solution. Goal programming: solving more complex problems. Scoring models. Analytic hierarchy process AHP. Establishing priorities using AHP. Using AHP to develop an overall priority ranking.
Numerical examples and application to marketing, finance, and operations management with LINGO.
Propedeuticità
Calculus I.
Prerequisiti e modalità di esame
Closed book exam
Metodi didattici
Lecture, tutorial, and lab.
Materiale didattico e bibliografia
Knut Sydsaeter, Peter Hammond, Atle Seierstad, Arne Strom, Further Mathematics for Economic Analysis, Financial Times Prentice Hall, 2008 (chapters 1,2,3).
Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, Kipp Martin, An Introduction to Management Science: Quantitative Approaches to Decision Making, Cengage Learning, 2010 (chapters 2,3,4,5,8,14).
Periodo
Primo trimestre
Periodo
Primo trimestre
Modalità di valutazione
Esame
Giudizio di valutazione
voto verbalizzato in trentesimi
Siti didattici
Docente/i
Ricevimento:
In aspettativa. Il ricevimento e' sospeso.
Stanza 30, DEMM