Checking date: 28/06/2021

Course: 2021/2022

Study: Master in Applied and Computational Mathematics (372)

Coordinating teacher: MOSCOSO CASTRO, MIGUEL ANGEL

Department assigned to the subject: Department of Mathematics

Type: Compulsory
ECTS Credits: 3.0 ECTS


Requirements (Subjects that are assumed to be known)
Students are expected to have a solid background in Linear Algebra and Calculus.
- To develop a theoretical basis and the skills for solving optimization problems arising in science and engineering. - To learn some of the more popular optimization toolboxes. Codes: CB6, CB7, CB8, CB9, CB10, CG2, CG4, CG5, CG6, CG7, CE1, CE2, CE3, CE4, CE8
Skills and learning outcomes
Description of contents: programme
1. Introduction to mathematical optimization. a. Classification of optimization problems. b. Geometric resolution of simple optimization problems. 2. Linear programming. a. Geometry interpretation b. The simplex method c. LP Duality 3. Quadratic optimization a. Geometrical examples b. Simplex method for quadratic optimization 4. Convex optimization. a. Convex sets and convex functions b. The Lagrange dual problem c. Optimality conditions d. Sensitivity Analysis e. Algorithms 5. Applications
Learning activities and methodology
- Theoretical sessions illustrated with different applications and examples. Material for out-of-class work. - Problem sessions to discuss different problems in science and engineering. There will be proposed projects to be solved at home.
Assessment System
  • % end-of-term-examination 30
  • % of continuous assessment (assigments, laboratory, practicals...) 70
Calendar of Continuous assessment
Basic Bibliography
  • S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press. 2004
Recursos electrónicosElectronic Resources *
Additional Bibliography
  • David G. Luenberger and Yinyu Ye. Linear and Nonlinear Programming. 3rd ed. Springer. 2008
  • Jorge Nocedal and Stephen J. Wright. Numerical Optimization. Springer-Verlag. 2006
  • R. Fletcher. Practical Methods of Optimization. Wiley. 1987
(*) Access to some electronic resources may be restricted to members of the university community and require validation through Campus Global. If you try to connect from outside of the University you will need to set up a VPN

The course syllabus and the academic weekly planning may change due academic events or other reasons.