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Under the strongly convex assumption, several recent works studied the globallinear convergence rate of the proximal incremental aggregated gradient (PIAG)method for minimizing the sum of a large number of smooth component functionsand a non-smooth convex function. In this paper, under \textsl{the quadraticgrowth condition}--a strictly weaker condition than the strongly convexassumption, we derive a new global linear convergence rate result, whichimplies that the PIAG method attains global linear convergence rates in boththe function value and iterate point errors. The main idea behind is toconstruct a certain Lyapunov function.

Linear Convergence of the Proximal Incremental Aggregated Gradient Method under Quadratic Growth Condition