  This paper is devoted to the design of efficient primal-dual algorithm (PDA)
for solving convex optimization problems with known saddle-point structure. We
present a new PDA with larger acceptable range of parameters and correction,
which result in larger step sizes. The step sizes are predicted by using a
local information of the linear operator and corrected by linesearch to satisfy
a very weak condition, even weaker than the boundedness of sequence generated.
The convergence and ergodic convergence rate are established for general cases,
and in case when one of the prox-functions is strongly convex. The numerical
experiments illustrate the improvements in efficiency from the larger step
sizes and acceptable range of parameters.
