Course Description: 

Matrix optimization has recently emerged as a promising research topic of its own because of a good number of high-profile applications, arising from finance, engineering, to social sciences. The lecturer will give a preliminary introduction of this advanced topic, often involving spectral analysis of matrices. To make it accessible to those who are not familiar to this area, this mini course will mainly focus on some particular examples and how they can be efficiently solved. If time permits, the lecturer will talk about its stability analysis and its numerical implications.

 

The structure of the talk:

1. Introduction and Mathematical background on Matrices

2. Three examples: Correlation matrix optimization, Euclidean distance matrix optimization and Time series of finite rank

3. Numerical methods: Alternating projection methods, Alternation direction method of multipliers (ADMM), Newton-CG method

4. Applications: Computing a valid correlation matrix in finance, Euclidean embedding in Multi-dimensional scaling and Molecular conformation, Hankel matrix optimization in time series

 

Time and Venue:

12/25:

15:00-17:00 at M212 

12/26:

10:00-12:00 at M310

14:00-15:00 at M212

M212 and M310, Mathematics Building, Department of Mathematics, NTNU