Final pensum in the course for spring 2019:
First of all, the pensum includes all the material and all the results and approaches that were discussed in the lectures. Summaries can be found here.
Lecture notes:
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Optimisation with convex constraints, in particular, the
necessary and sufficient conditions for optimisation with convex constraints, the idea of
projections, and
Slater's constraint qualification.
Lagrangian duality, in particular, the notion of
dual optimisation problems,
weak duality, the notion of
saddle points,
Slater's constraint qualification, and
strong duality for convex programmes.
All the exercises.
The following chapters in Nocedal & Wright, Numerical Optimization, Second Edition, 2006 (most important points in boldface):
Basics of optimization: Chap. 1, 2.
Line Search Methods: Chap. 3.1-3.3.
Trust-Region Methods: Chap. 4.1-4.3.
Conjugate Gradient Methods: Chap. 5.
Quasi-Newton Methods: Chap. 6.1, 6.4.
Least-Squares Problems: Chap. 10.1-10.3.
Constrained Optimization: Chap. 12.1-12.5, 12.9.
Linear Programming: Chap. 13.1-13.2, 14.1.
Quadratic Programming: Chap. 16.1, 16.4, 16.5, 16.7.
Penalty Methods: Chap. 17.1-17.3.
Sequential Quadratic Programming: Chap. 18.1-18.3 (and 15.5).
Interior-Point Methods for Nonlinear Programming: Chap. 19.1, 19.6.
Note: Programming is not part of the exam; this part of the lecture has already been covered by the project.