Seminár z kvalitatívnej teórie diferenciálnych rovníc

Seminar on Qualitative Theory of Differential Equations

Thursday 14.11.2013 at 14:15 Lecture room M-223

Daniel Sevcovic (KAMŠ FMFI UK):

Solution to the inverse Wulff problem by means of the enhanced semidefinite relaxation method

Abstract:

We propose a method for resolving the optimal anisotropy function. The method is based on resolving the optimal anisotropy function as a minimizer of the anisoperimetric ratio for a given Jordan curve in the plane. It can be viewed as a solution to the inverse Wulff problem. It leads to a nonconvex quadratic optimization problem with linear matrix inequalities. We solve this nonlinear programming problem by means of the so-called enhanced semidefinite relaxation method. It consisted in solving a convex semidefinite problem obtained by a semidefinite relaxation of the original problem. We show that the sequence of finite dimensional approximations of the optimal anisoperimetric ratio converges to the optimal anisoperimetric ratio which is a solution of the inverse Wulff problem. Several computational examples, including those corresponding to real snowflakes boundaries and discussion on the rate of convergence of numerical method will be also presented in this talk. This is joint work with M.Trnovska.