Optimization (2008/2009)

Course not running

Course code
4S00263
Name of lecturer
Letizia Pellegrini
Number of ECTS credits allocated
6
Academic sector
SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES
Language of instruction
Italian
Period
2° Q dal Jan 26, 2009 al Mar 27, 2009.

Lesson timetable

2° Q
Day Time Type Place Note
Wednesday 8:30 AM - 10:30 AM lesson Lecture Hall C from Feb 5, 2009  to Mar 27, 2009
Wednesday 10:30 AM - 12:30 PM lesson Lecture Hall G  
Thursday 4:30 PM - 6:30 PM lesson Lecture Hall I from Jan 29, 2009  to Jan 29, 2009
Friday 8:30 AM - 10:30 AM lesson Lecture Hall B  

Learning outcomes

The aim of the course is to treat nonlinear optimization problems by looking into the theoretical analysis tools and the solution methods.

Syllabus

1. Fundamental Concepts
Optimization problems. Convex sets and convex functions. Some extensions of convexity. Linear support and separation of sets. Cones and polyhedral convexity. Alternative theorems. Subgradient and subdifferential.

2. Uncostrained Optimization and Optimization over a Convex Set
Outline of monodimensional optimization. The Newton method. Gradient methods. The conjugate directions method and the conjugate gradient method. The feasible directions methods. Linearization methods: the method of Frank and Wolfe. The gradient projection method.

3. Multipliers Theory
Necessary conditions. Equality constraints; Lagrange multipliers. Inequality constraints; Kuhn-Tucker multipliers. Regularity conditions and constraints qualification. John multipliers. The perturbation function. The meaning of the multipliers; economic intepretation. Sufficient conditions. Saddle point of a function. Saddle point conditions and minimum points.

4. Lagrangian Duality
The dual problem. Dual variables and Lagrange multipliers. Weak and strong duality theorems. Convex and nonconvex problems. Some applications.

Reference books
Author Title Publisher Year ISBN Note
M.Minoux Mathematical Programming: theory and algorithms John Wiley and Sons 1986 0471901709
D.M.Bertsekas Nonlinear Programming Athena Scientific 2004 1886529140

Assessment methods and criteria

Written and oral final examination.

Teaching aids

Documents

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