1.

On factorization of non-commutative polynomials by semidefinite programming.

I gave the lecture at the most important optimization conference International symposium on mathematical programming, which is organized every third year. I presented the recent results about non-commutative polynomials, obtained while the post-doc project.

B.03 Paper at an international scientific conference

COBISS.SI-ID: 1024052801

2.

NCsostools - an opensource software package to handle the noncommutative polynomials.

We wrote a Matlab package NCsostools which contains routines to handle the NC polynomials (multiplication, addition, power, simplification etc.) , and routines to detect whether given NC polynomial is SOHS (modulo cyclic equivalence). A routine to find rational SOHS decomposition for NC polynomials with rational coefficients is provided as well as a routine for extracting the minimum of trace of NC polynomial. The package is available from http://ncsostools.fis.unm.si/.

F.23 Development of new system-wide, normative and programme solutions, and methods

COBISS.SI-ID: 15233369

3.

Information society and information technology 2009

The conference covered wide range of topics from information society and information technology.

B.02 Presiding over the programming board of a conference

COBISS.SI-ID: 23008807

4.

10th Symposium on operations research in Slovenia.

At the conference best regional applied mathematicians meets. As a result there is published a conference proceedings with peer review papers and a special issue of Central European Journal of Operations Research, which is an SCII journal and is currently under preparation.

B.01 Organiser of a scientific meeting

COBISS.SI-ID: 1024060481

5.

Contribution of copositive formulations to graph partitioning problem

This paper provides analysis of several copositive formulations of the Graph partitioning problem (GPP) and semidenite relaxations based on them. We prove that the copositive formulations based on results from Burer and Povh are equivalent and that they both imply semidefinite relaxations which are stronger than the Donath-Homan eigenvalue lower bound and projected semidefinite lower bound from Wolkowicz and Zhao.