Optimization

Recommended Prerequisites

Basic knowledge of Linear Algebra, Algebra, Mathematical Analysis, and Numerical Analysis.

Teaching Methods

The classes are essentially of expository style and include examples and exercises to apply the material being taught. Extensive tutorial time is offered to the students to support the solution of the homework assignments and preparation for the various exams.

Learning Outcomes

The main goal is teaching the optimization theory, from conic programming (and some of its best-known particularizations) to non-linear and non-smooth programming, and the convergence properties of the main numerical for continuous optimization, using convex, differential, and non-smooth analyses. The course aims at developing the following skills: knowledge of mathematical results; ability to generalize and abstract; logical thinking; competence in using computational tools. On the personal level it also allows to develop self-learning skills and independent thinking.

Work Placement(s)

No

Syllabus

Optimality conditions and duality theory for conic, convex, non-linear, non-differentiable and multi-objective optimization. Depending on the approach to the course, other topics might be considered, such as numerical methods for continuous optimization, algebraic methods and representability in polynomial optimization and semi-definite programming, or continuous relaxations for combinatorial problems.

Head Lecturer(s)

João Eduardo da Silveira Gouveia

Assessment Methods

Continuous assessment
Resolution Problems: 25.0%
Frequency: 75.0%

Continuous assessment
Frequency: 50.0%
Resolution Problems: 50.0%

Final assessment
Exam: 100.0%

Bibliography

A. Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, MOS-SIAM Series on Optimization, SIAM, Filadélfia, 2001.

G. Blekherman, P.A. Parrilo and R. Thomas, Semidefinite Optimization and Convex Algebraic Geometry,

MOS-SIAM Series on Optimization, SIAM, Filadélfia, 2013.

I. Griva, S.G. Nash, and A. Sofer, Linear and Nonlinear Optimization, 2nd edition, SIAM, Filadélfia, 2009.

J. Nocedal and S.J. Wright, Numerical Optimization, 2nd edition, Springer Series in Operations Research, Springer, Berlim, 2006.