OPTIMIZATION


Ph.D. programs in Mathematical Engineering and Business Administration and Quantitative Methods

 

Group:

Mondays and Thursdays from 16:00 to 18:00.

Classroom: 7.3.J.08 (Leganés).

 

Professor:

Javier Nogales


OBJECTIVES:
After the course, the student must become familiar with the modeling and the application of optimization methods in complex decision-making processes. The complexity of these processes has grown in the last years and, hence this course tries to provide the necessary tools and modern techniques of optimization for the efficient resolution of many decision-making problems arising in diverse areas like Business, Marketing, Finance and Engineering.

PROGRAM:
1. Introduction (4 sessions) Modeling (air traffic control, portfolio optimization, support vector machines, advanced estimation procedures and revenue management) and basic properties
2. Unconstrained Optimization (3 sessions) Optimality characterization, basic algorithms, local convergence, large-scale problems
3. Constrained Optimization (3 sessions) General properties, necessary and sufficient conditions, basic algorithms
4. Optimization under Uncertainty (4 sessions) Stochastic Programming, Chance Constraints, Robust Optimization, Applications

EVALUATION CRITERIA:
Continuous evaluation along the course: it consists of 4 homeworks (theoretical and practical) and a final project.

Final grade = Participation class (5%) + Homework 1 (10%) + Homework 2 (15%) + Homework 3 (15%) + Homework 4 (15%) + Final project (35%) + Project evaluation (5%)

It is recommendable that students plan the final project from the beginning of the course.

MAIN REFERENCES:

Most of the course program can be followed through the teaching material (slides) provided before each topic. Moreover, the following two books are available (for free) through internet and cover almost all the topics.

Convex Optimization by Boyd and Vandenberghe

Lecture Notes on Stochastic Programming by Ruszczynski and Shapiro

OTHER REFERENCES:
- J. Nocedal and S.J. Wright: Numerical Optimization. Springer-Verlag, 2006
- D.B. Bertsekas: Nonlinear Programming. Athena Scientific, 1999
- G.N. Nash and A. Sofer: Linear and Nonlinear Programming. McGraw-Hill, 1996
- S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004.
- A.R. Conn, N.I.M. Gould y Ph. Toint: Trust-region methods. SIAM publications, 2000
- P.E. Gill, W. Murray and M.H. Wright: Practical Optimization. Academic Press, 1981
- J.R. Birge and Francois Louveaux: Introduction to Stochastic Programming. Springer-Verlag, 1997
- A. Ruszczynski, A. Shapiro (Ed.): Stochastic Programming. Elsevier , 2003
- Stein W. Wallace (Ed.): Applications of Stochastic Programming. Book Data Limited, UK, 2005
- William T. Ziemba and Raymond G. Vickson (Ed.): Stochastic optimization models in finance. World Scientific, 2006
- Gerard Cornuejols and Reha Tütüncü: Optimization Methods in Finance. Cambridge University Press, 2007

TEACHING MATERIAL:

  It is recommendable to print 4 slides per page. (Computer Lab material coming soon.)

 

Introduction:    intro.pdf

Unconstrained Optimization :   T1.pdf

Constrained Optimization :   T2.pdf

Optimization under Uncertainty :   T3.pdf

 

  Homework 1     Deadline: October, 6

  Homework 2    Deadline: October, 17

  Homework 3    Deadlilne: October, 27

  Homework 4    Deadlilne: ż?

  Final Project    Presentation: November, 24 (it must be submitted on November, 21)

Commentaries and Suggestions: Javier Nogales FcoJavier.Nogales@uc3m.es
Last modification: 16/10/2011