Conic programming and applications

Conic programming and applications

Members of the research team from the DAMS

  • doc. RNDr. Margaréta Halická, CSc.
  • doc. RNDr. Mária Trnovská, PhD.
  • prof. RNDr. Daniel Ševčovič, DrSc.
  • Mgr. Terézia Fulová
  • Mgr. Jakub Hrdina

The aim of the research is to provide qualitative and numerical analysis of solutions of direct and inverse variational problems, which can be solved using modern methods of conic programming. We focus on the analysis of of strong duality properties of primal and dual pairs in case of conic programming problems.

Selected papers

  1. M. Halická, P. Jurča: On the sustainable growth in an economy with perfectly substituable exhaustible resources, Natural Resource Modeling 26 (2013), No 3, 403-434.
  2. M. Halická, M. Trnovská, The Russell measure model: Computational aspects, duality, and profit efficiency, European Journal of Operational Research, 268(1), 2018, 386-397.
  3. Halická, M., Trnovská, M.: Limiting behaviour and analyticity of weighted central paths in semidefinite programming, Optimization Methods and Software, 25(2), 2010, 247-262.
  4. D. Ševčovič and M. Trnovská: Solution to the Inverse Wulff Problem by Means of the Enhanced Semidefinite Relaxation Method, Journal of Inverse and III-posed Problems 23(3) 2015, 263-285.
  5. D. Ševčovič and M. Trnovská: Application of the Enhanced Semidefinite Relaxation Method to Construction of the Optimal Anisotropy Function, IAENG International Journal of Applied Mathematics 45(3) (2015), 227-234.
  6. S. Pavlíková, D. Ševčovič: On a Construction of Integrally Invertible Graphs and their Spectral Properties, Linear Algebra and its Applications, 532 (2017), 512-533.
  7. S. Pavlíková, D. Ševčovič: Maximization of the Spectral Gap for Chemical Graphs by means of a Solution to a Mixed Integer Semidefinite Program, Computer Methods in Materials Science, 4 2016, 169-176.