All programmes > Optimization

Optimization (B-KUL-H03E3A)

6 ECTSEnglish50 First termCannot be taken as part of an examination contract
Patrinos Panos
POC Wiskundige ingenieurstechnieken

Aims

The course gives insight into the mathematical formulation of optimization problems and deals with advanced methods and algorithms to solve these problems. The knowledge of the possibilities and shortcomings of these algorithms should lead to a beter understanding of their applicability in solving concrete engineering problems. In the course, an overview of existing software for optimization will also be given, this software will be used in the practical exercise sessions. The student learns to select the appropriate solving methods and software for a wide range of optimization problems and learns to correctly interpret the results.

The following knowledge and skills will be acquired during this course:

  • The student will be able to formulate a mathematical optimization problem starting from a concrete engineering problem.
  • The student will be able to classify optimization problems into appropriate categories (e.g., convex vs. non-convex problems).
  • The student will be familiar with different optimization strategies and their properties, and will hence be able to decide which strategy to use for a given optimization problem.
  • The student will be able to formulate the optimality conditions for a given optimization problem.
  • The student will have a profound understanding of a wide variety of optimization algorithms and their properties, and will be able to apply the appropriate algorithms for a given optimization problem.
  • The student will be familiar with state-of-the-art optimization software packages, and will be able to use these in an efficient manner.

Previous knowledge

Skills: the student should be able to analyze, synthesize and interpret.
Knowledge: Analysis, Numerical mathematics, Numerical linear algebra.

Order of Enrolment


This course unit is a prerequisite for taking the following course units:
H0T46A : Project Mathematical Engineering

Identical courses

This course is identical to the following courses:
H0S15A : Optimalisatie

Is included in these courses of study

Activities

4 ects. Optimization: Lecture (B-KUL-H03E3a)

4 ECTSEnglishFormat: Lecture30 First term
Patrinos Panos
POC Wiskundige ingenieurstechnieken

Content

1. Introduction
- a number of motivating examples (control, fitting, planning)
- mathematical modelling of optimization problems
- the importance of convexity
- classification of optimization problems
2. Algorithms for continuous optimization without constraints
- the two basic strategies: line search or trust region techniques
- gradient-based techniques: the steepest gradient and the added gradient method
- Newton and quasi-Newton techniques
- special methods for non-linea least square problems
3. Algorithms for continuous optimization with constraints
- the KKT-optimization conditions
- algorithms for linear problems: simplex-method and primal-dual interior point method
- algorithms for quadratic problems: active-set technique and interior point method
- convex optimization: formulation, the concept duality, algorithms
- general non-linear optimization (penalizing and barrier techniques, connection to interior point algorithms)

4. Introduction to global optimization methods
- deterministic methods (branch and bound, ...)
- stochastic and heuristic methods (Monte Carlo methods, simulated annealing, evolutionary algorithms, swarm-based algorithms,...)

5. Software
- discussion of the possibilities of the most current optimization software-packages
- sources on the internet: the Network Enabled Optimization Server

Course material

Study cost: 1-10 euros (The information about the study costs as stated here gives an indication and only represents the costs for purchasing new materials. There might be some electronic or second-hand copies available as well. You can use LIMO to check whether the textbook is available in the library. Any potential printing costs and optional course material are not included in this price.)

- Numerical Optimization, J. Nocedal and S. Wright, Springer, New York, 1999.
- Optimization Software Guide, J. Moré and S. Wright, SIAM, Philadelphia, 1993.

Is also included in other courses

2 ects. Optimization: Exercises and Laboratory Sessions (B-KUL-H03E4a)

2 ECTSEnglishFormat: Practical20 First term
Patrinos Panos
POC Wiskundige ingenieurstechnieken

Content

Exercises and lab sessions with the course Optimisation

Evaluation

Evaluation: Optimization (B-KUL-H23E3a)

Type : Exam during the examination period
Description of evaluation : Written
Type of questions : Open questions

Explanation


- part I, theory (closed-book with use of formulary) 
- part II, exercises (Open-book on computer; example programs are available)