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doc. dr. Janez Povh

doc. dr. Janez Povh

Dekan Fakultete za informacijske študije

Govorilne ure: ob ponedeljkih in sredah v prostorih FIŠ na Novem trgu 5 (prosim za predhodno najavo po elektronski pošti).

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Telefon: +386  (0) 7  37 37  884

E-mail: janez.povh at fis.unm.si

Bibliografija: COBISS šifra 22649

Short biography:

Janez Povh finished undergraduate study in applied mathematics in 1998 and received Ph.D. from mathematics in 2006, both at University in Ljubljana, Faculty of mathematics and physics. He prepared his dissertation Application of semidefinite and copositive programming in combinatorial optimization under supervision of Franz Rendl from Institute of mathematics at Alpen Adria University Klagenfurt, Austria.

Currently he is working on:                                                                                                                                        

  • application of semidefinite programming to obtain a sum of hermitian squares (SOHS) decomposition of real non-commutative polynomials;
  • semidefinite approximations of the cone of copositive matrices;
  • copositive representations of NP hard optimization problems.

Awards:

He received Krka prize for the research published in the disssertation.

Predavanja/Teaching

  • Matematika 1/Mathematics 1,

  • Matematika 2/Mathematics 2,

  • Statistika 2/Statistics 2,

  • Multivariatna analiza/Multivariate analysis.

Projekti/Projects

  • Topological and metric graph theory - financed by Slovene research agency (Institute of Mathematics, Physics and Mechanics Ljubljana, Slovenia)

  • Algorithms for allocations assignment - financed by Slovene research agency                      (Institute of Mathematics, Physics and Mechanics Ljubljana, Slovenia)

  • Algorithmic Discrete Optimization Network - Adonet –EU (Alpen Adria University Klagenfurt, Austria),

  • New methods development and application of existing mathematical programming methods in combinatorial optimization and real algebra - financed by Slovene research agency (Institute of Mathematics, Physics and Mechanics Ljubljana, Slovenia).

Izbrana predavanja/selected lectures:

Ncsostools: a computer algebra system for symbolic and numerical computation with nc polynomials (Positivity, Valuations and Quadratic Forms, Konstanz, October 1-6)

On factorization of non-commutative polynomials by semidefinite programming (Ismp 2009, Chicago, 25. 8. 2009)

On approximations of quadratic programs over the orthogonal matrices (7th Europt workshop: Advances in continuous optimization, Remagen, 3.-4. 7. 2009)

On factorization and optimization of noncommutative polynomials with NCSOStools (Klagenfurt, 30. 4. 2009)

SOHS decomposition of a non-commutative polynomials: find it by NCSOStools (Vocal 2008, Veszprem, 1. 12. 2008, Hungary)

NCsostools for SOHS decompositions of non-commutative polynomials (KOI2008, Pula, 25. 8. 2008, Croatia).

Iskanje SOS in SOHS razcepov s semidefinitnim programiranjem (Seminar for graphs and algorithms, Faculty for mathematics and physics Ljubljana, March 6th, 2008)

The power of copositive programming (CFG 07 Conference, Heidelberg, September 17-21, 2007)

On approximations of hard combinatorial problems by semidefinite and copositive programming (invited lecture at University of Vienna, Faculty of economics, November 5th, 2007)

What can be done with copositive programming (invited lecture at Eötvös Loránd University , June 5th, 2007)

Izbrana bibliografija/selected publications:

  • Sabine Burgdorf, Krisitijan Cafuta, Igor Klep, Janez Povh: Semidefinite Programming Certificates For Tracial Matrix Inequalities, submitted, 2010 (paper).
  • Krisitijan Cafuta, Igor Klep, Janez POvh: On the nonexistence of sum of squares certificates for the BMV conjecture, submitted, 2009 (paper).
  • Janez Povh: Towards the optimum by semidefinite programming, VDM Verlag, 2009.
  • Igor Klep, Janez Povh: Semidefinite programming and sums of hermitian squares of noncommutative polynomials, Journal of Pure and Applied Algebra 214 (2010) 740-749 ( paper).
  • Kristjan Cafuta, Igor Klep, Janez Povh: Ncsostools: a computer algebra system for symbolic and numerical computation with noncommutative polynomials, submitted (paper).
  • Janez Povh: Semidefinite approximations for quadratic matrix programs over orthogonal matrices, to appear in Journal of global optimization, 2010 (paper)
  • Janez Povh, Franz Rendl: Approximating non-convex quadratic programs by semidefinite and copositive programming. KOI 2006 proceedings, p. 35-45, Pula, 2008. http://oliver.efpu.hr/koi06/koi06_proceedings.pdf. (paper)
  • Janez Povh: On decompositions of real polynomials using mathematical
    programming methods,     submitted, 2008. (paper)
  • Jerome Malick, Janez Povh, Franz Rendl, Angelika Wiegele: Regularization methods for semidefinite programming, SIAM J. Optim., vol. 20, 336-356, 2009 . (paper)
  • Janez Povh, Franz Rendl: Copositive and Semidefinite Relaxations of the Quadratic Assignment Problem, Discrete Optimization, Vol. 6, 231-24, 2009. (paper, link to published paper)
  • Janez Povh, Franz Rendl: A copositive programming approach to graph partitioning, SIAM j. optim. (Print), 18, 2007, 223-241. (paper)
  • Janez Povh, Franz Rendl, Angelika Wiegele: A boundary point method to solve semidefinite programs. Computing, 2006, vol. 78, no. 3, str. 277-286. (paper)

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