  The incremental aggregated gradient algorithm is popular in network
optimization and machine learning research. However, the current convergence
results require the objective function to be strongly convex. And the existing
convergence rates are also limited to linear convergence. Due to the
mathematical techniques, the stepsize in the algorithm is restricted by the
strongly convex constant, which may make the stepsize be very small (the
strongly convex constant may be small).
  In this paper, we propose a general proximal incremental aggregated gradient
algorithm, which contains various existing algorithms including the basic
incremental aggregated gradient method. Better and new convergence results are
proved even with the general scheme. The novel results presented in this paper,
which have not appeared in previous literature, include: a general scheme,
nonconvex analysis, the sublinear convergence rates of the function values,
much larger stepsizes that guarantee the convergence, the convergence when
noise exists, the line search strategy of the proximal incremental aggregated
gradient algorithm and its convergence.
