We propose a modification of the classical proximal point algorithm for finding zeroes of a maximal monotone operator in a Hilbert space. In particular, an approximate proximal point iteration is used to construct a hyperplane which strictly separates the current iterate from the solution set of the problem. This step is then followed by a projection of the current iterate onto the separating h...

This paper proposes a two-point inertial proximal point algorithm to find zero of maximal monotone operators in Hilbert spaces. We obtain weak convergence results and non-asymptotic O(1/n) rate our proposed non-ergodic sense. Applications various well-known convex optimization methods, such as the method multipliers alternating direction are given. Numerical given demonstrate accelerating behav...

We prove an abstract form of the strong convergence Halpern-type and Tikhonov-type proximal point algorithms in CAT(0) spaces. In addition, we derive uniform computable rates metastability (in sense Tao) for these iterations using proof mining techniques.

We present several strong convergence results for the modified, Halpern-type, proximal point algorithm xn+1 = αnu + (1 − αn)Jβn xn + en (n = 0, 1, . . .; u, x0 ∈ H given, and Jβn = (I + βn A)−1, for a maximal monotone operator A) in a real Hilbert space, under new sets of conditions on αn ∈ (0, 1) and βn ∈ (0,∞). These conditions are weaker than those known to us and our results extend and impr...