Relatively inexact proximal point algorithm and linear convergence analysis (Q963522)

Summary: Based on a notion of relatively maximal \((m)\)-relaxed monotonicity, the approximation solvability of a general class of inclusion problems is discussed, while generalizing \textit{R. T. Rockafellar}'s theorem [Math. Oper. Res. 1, 97--116 (1976; Zbl 0402.90076)] on linear convergence using the proximal point algorithm in a real Hilbert space setting. Convergence analysis, based on this new model, is simpler and more compact than that of the celebrated technique of Rockafellar in which the Lipschitz continuity at 0 of the inverse of the set-valued mapping is applied. Furthermore, it can be used to generalize the Yosida approximation, which, in turn, can be applied to first-order evolution equations as well as evolution inclusions.