Special Lecture on Mathematical and Information Sciences II

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Kim Sunyoung 
Tue3-4(W832)  Tue7-8(W832)  
Lecture2  Exercise0  Experiment0
Syllabus updated
Lecture notes updated
Fall Semester

Outline of lecture

Numerical linear algebra and conic optimization

Purpose of lecture

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, semide nite programming and recent advances
in completely positive programming will be discussed.

Plan of lecture

Lecture 1 What is Numerical Linear Algebra? linear algebra-historical notes,
one application
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 de nite 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 de cient system
Givens rotation
Lecture 9-10 Semide nite programming: theory and applications
Lecture 11-12 Semide nite programming: theory and applications
Lecture 13-14 Semide nite programming: theory and applications
Lecture 15 Comptely positive programming, doubly nonnegative programming
Lecture 16 Exam

Textbook and reference

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.

Related and/or prerequisite courses

Background in linear algebra and Matlab programming.


One closed book exam

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