Package volesti supports volume estimation for polytopes, providing several randomized approximation methods. The most efficient implementation employs billiard walk (uniform sampling) and a certain Multiphase Monte Carlo technique. The project is about extending volesti to support uniform and gaussian sampling for spectrahedra. Moreover, we will extend the volume estimation methods to support spectrahedra. Spectrahedra are probably the most well studied shapes after polyhedra. They are the feasible regions of semidefinite programs in the way that polytopes are feasible regions of linear programs. Thus, the project is of special interest for the research communities of geometric computing and optimization.

Organization

Student

Alexandros Manochis

Mentors

  • Apostolos Chalkis
  • Vissarion Fisikopoulos
  • Elias
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2021