In this paper we reformulate the “Oblique Extension Principle” as a
problem of semi-definite programming. Using this technique we show,
that the existence of a tight frame is equivalent to the existence of a
certain matrix from a cone of positive semi-definite matrices, whose
entries satisfy linear constraints. We show how to use the optimization
techniques to minimize the number of frame generators in univariate
and multivariate cases. We apply our results for constructing tight
frames for several subdivision schemes.