  This paper considers the problems of unconstrained minimization of large
scale smooth convex functions having block-coordinate-wise Lipschitz continuous
gradients. The block coordinate descent (BCD) method are among the first
optimization schemes suggested for solving such problems
\cite{nesterov2012efficiency}. We obtain a new lower (to our best knowledge the
lowest currently) bound that is $16p^3$ times smaller than the best known on
the information-based complexity of BCD method based on an effective technique
called Performance Estimation Problem (PEP) proposed by Drori and Teboulle
\cite{drori2012performance} recently for analyzing the performance of
first-order black box optimization methods. Numerical test confirms our
analysis.
