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The incremental aggregated gradient algorithm is popular in networkoptimization and machine learning research. However, the current convergenceresults require the objective function to be strongly convex. And the existingconvergence rates are also limited to linear convergence. Due to themathematical techniques, the stepsize in the algorithm is restricted by thestrongly convex constant, which may make the stepsize be very small (thestrongly convex constant may be small).  In this paper, we propose a general proximal incremental aggregated gradientalgorithm, which contains various existing algorithms including the basicincremental aggregated gradient method. Better and new convergence results areproved 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 whennoise exists, the line search strategy of the proximal incremental aggregatedgradient algorithm and its convergence.

General Proximal Incremental Aggregated Gradient Algorithms: Better and Novel Results under General Scheme