Numerical linear algebra and conic optimization
We will give a brief introduction to the basic ideas of numerical linear
algebra and conic optimization. The rst part of this course will cover topics from
numerical linear algebra that are necessary for the implementation of optimization
methods. Numerical solutions of linear systems, matrix factorizations, and least
squares methods will be discussed from the theoretical and algorithmic aspects. The
second part of the course will be devoted to the optimization methods, focusing on
conic programming. In particular, semidenite programming and recent advances
in completely positive programming will be discussed.
Lecture 1 What is Numerical Linear Algebra? linear algebra-historical notes,
Lecture 2 Notation, basic concepts in Numerical Linear Algebra,
range, null space, matrix and vector norms
Lecture 2-3 Linear Equations: Gaussian elimination, pivoting
Lecture 4 Positive denite systems,
Sparse systems, banded systems
Lecture 5-6 Orthogonalization and Least squares problems
Singular value decomposition, QR factorization, Householder orthogonalization
Lecture 7-8 Nearly rank decient system
Lecture 9-10 Semidenite programming: theory and applications
Lecture 11-12 Semidenite programming: theory and applications
Lecture 13-14 Semidenite programming: theory and applications
Lecture 15 Comptely positive programming, doubly nonnegative programming
Lecture 16 Exam
An Introduction to Numerical Analysis by Endre Suli and
David Mayers, Cambridge, 2003.
Numerical Linear Algebra by Lloyd N. Trefethen and David Bau, III, SIAM, 1997.
Convex Optimization by Stephen P. Boyd, Cambridge, 2004.
Background in linear algebra and Matlab programming.
One closed book exam