Optimization (2007/2008)

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 10, 2008 al Mar 12, 2008.

Lesson timetable

2° Q
Day Time Type Place Note
Monday 2:30 PM - 4:30 PM lesson Lecture Hall B  
Tuesday 11:30 AM - 1:30 PM lesson Lecture Hall B  
Wednesday 8:30 AM - 10:30 AM lesson Lecture Hall C  

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 cones. Linear support and separation of sets. Convex functions. Some extensions of convexity. Subgradient and subdifferential. Alternative theorems.

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

3. Multipliers Theory
Necessary conditions. Equality constraints, Lagrange multipliers. Regularity conditions. John multipliers. The general case; Karush-Kuhn-Tucker multipliers. Sufficient conditions. Saddle point conditions and minimum points.

4. Duality and Complementarity
The dual problem. Dual variables and Lagrange multipliers. Weak and strong duality. Nonlinear problems. Quadratic problems. Complementarity systems and complementarity problems.

5. Quadratic Programming
The convex case. The modified simplex method. Geometric interpretation. Other solution methods in the convex case. Some applications.

Reference books
Author Title Publisher Year ISBN Note
F.Giannessi Constrained Optimization and Image Space Analysis, Volume 1: Separations of Sets and Optimality Springer 2005 038724770X
M.Minoux Mathematical Programming: theory and algorithms John Wiley and Sons 1986 0471901709
M.Pappalardo, M.Passacantando Metodi e modelli matematici di ottimizzazione per la gestione Edizioni plus, Pisa university press 2004 888492166X
D.M.Bertsekas Nonlinear Programming Athena Scientific 2004 1886529140

Assessment methods and criteria

Written and oral final examination.

Teaching aids

Documents

Studying