Strongly Convergent Inertial Proximal Point Algorithm Without On-line Rule

We present a strongly convergent Halpern-type proximal point algorithm with double inertial effects to find a zero of a maximal monotone operator in Hilbert spaces. The strong convergence results are obtained without on-line rule of the inertial parameters and the iterates. This makes our proof arguments different from what is obtainable in the literature where on-line rule is imposed on a strongly convergent proximal point algorithm with inertial extrapolation. Numerical examples with applications to image restoration and compressed sensing show that our proposed algorithm is useful and has practical advantages over existing ones.