  For interior-point algorithms in linear programming, it is well-known that
the selection of the centering parameter is crucial for proving polynomility in
theory and for efficiency in practice. However, the selection of the centering
parameter is usually by heuristics and separate from the selection of the
line-search step size. The heuristics are quite different while developing
practically efficient algorithms, such as MPC, and theoretically efficient
algorithms, such as short-step path-following algorithm. This introduces a
dilemma that some algorithms with the best-known polynomial bound are least
efficient in practice, and some most efficient algorithms may not be
polynomial. In this paper, we propose a systematic way to optimally select the
centering parameter and line-search step size at the same time, and we show
that the algorithm based on this strategy has the best-known polynomial bound
and may be very efficient in computation for real problems.
