  This paper proposes a unique optimization approach for estimating the minimax
rational approximation and its application for evaluating matrix functions. Our
method enables the extension to generalized rational approximations and has the
flexibility of adding constraints. In particular, the latter allows us to
control specific properties preferred in matrix function evaluation. For
example, in the case of a normal matrix, we can guarantee a bound over the
condition number of the matrix, which one needs to invert for evaluating the
rational matrix function. We demonstrate the efficiency of our approach for
several applications of matrix functions based on direct spectrum filtering.
