  In this paper we propose and apply the enhanced semidefinite relaxation
technique for solving a class of non-convex quadratic optimization problems.
The approach is based on enhancing the semidefinite relaxation methodology by
complementing linear equality constraints by quadratic-linear constrains. We
give sufficient conditions guaranteeing that the optimal values of the primal
and enhanced semidefinite relaxed problems coincide. We apply this approach to
the problem of resolving the optimal anisotropy function. The idea is to
construct an optimal anisotropy function as a minimizer for the anisotropic
interface energy functional for a given Jordan curve in the plane. We present
computational examples of resolving the optimal anisotropy function. The
examples include boundaries of real snowflakes.
