TMA 4180 Optimeringsteori

Survey of the curriculum 2011Ê

Some general advice about the exam:

Ê

The curriculum is found in the following material

Ê

  1. J. Nocedal and S.J. Wright: Numerical Optimization, 2nd Ed., Springer, 2006
  2. J.L. Troutman: Variational Calculus and Optimal Control, 2nd Ed., Springer, 1996
  3. A subset of the supplementary notes (see below)
  4. Exercises with the solutions

Ê

Note: Even if his list below is fairly detailed, Òcentral conceptsÓ may not be quite complete!

Ê

NB! Page number according to N&W Ed. 2Ê(differs from Ed. 1!)

1 Unconstrained Optimization

Nocedal & Wright and supplementary notes:

Ê

Section 2.1, 2.2 (survey only)

Central concepts:

Ê

Section 3.1 - 3.3 (to p. 48)

Central concepts:

Ê

Section 4.1 (to p. 76)

Central concepts:

Ê

Section 5.1, 5.2 (to p. 122)

Central concepts:

Ê

Section 6.1, 6.2 

Central concepts:

Ê

Section 10.1 - 10.3 (to p. 262)

Central concepts:

Ê

2 Constrained optimization

Section 12.1, 12.2, 12.3, 12.5

The supplementary note about the KKT-theorem covers all the theory.Ê

Central concepts:


ÊSection 13.1, 13.2, 13.3, p. 378 Ð 382.

The supplementary note about LP cover the curriculum.

ÊCentral concepts:



Section 16.1, 16.2, 16.4 (to p. 465), p. 472-475 (Example), 16.7 (the idea)

The supplementary notes cover the curriculum.

Central concepts:


ÊSection 17.1, 17.2 (to p. 511)

The note covers the curriculum.

ÊCentral concepts:


3 Variational Calculus

From Troutman.

ÊChapter 2.1, 2.2, 2.3, 2.4.

ÊCentral concepts:


ÊChapter 3.1, 3.2, 3.3, 3.4, 3.5

ÊCentral concepts:


3 Notes

All notes mentioned above are available on the Web page.

Some of the notes contain detailed proofs. These are not part of the curriculum.

Ê

Ê

4 Exercises

All analytical exercises and solutions are part of the curriculum (Not problems requiring numerical methods!)