Optimization

A.Y. 2017/2018
6
Max ECTS
40
Overall hours
SSD
SECS-S/06
Language
English
Learning objectives
Students will learn advanced optimization methods and how to use them to model and solve problems in economics and social sciences.
Expected learning outcomes
Undefined
Course syllabus and organization

Single session

Responsible
Lesson period
First trimester
ATTENDING STUDENTS
Course syllabus
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. 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. Extreme points. Local extreme points. Equality constraints: the Lagrange problem. Local second-order conditions. Inequality constraints: nonlinear programming. Sufficient conditions. Nonnegativity constraints. Concave programming. Existence of Lagrange multipliers.
NON-ATTENDING STUDENTS
Course syllabus
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. 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. Nonnegativity constraints. Concave programming. Existence of Lagrange multipliers.
SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES - University credits: 6
Lessons: 40 hours
Professor(s)
Reception:
On leave. Office hours are suspended.
Reception:
Tuesday from 2.30 p.m. to 5.30 p.m.
Microsoft office Teams (https://work.unimi.it/servizi/servizi_tec/1536.htm)