Approximating solutions of maximal monotone operators in Hilbert spaces
Journal of Approximation Theory
A Regularization Method for the Proximal Point Algorithm
Journal of Global Optimization
A note on a paper "A regularization method for the proximal point algorithm"
Journal of Global Optimization
On the contraction-proximal point algorithms with multi-parameters
Journal of Global Optimization
Journal of Global Optimization
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We present several strong convergence results for the modified, Halpern-type, proximal point algorithm $${x_{n+1}=\alpha_{n}u+(1-\alpha_{n})J_{\beta_n}x_n+e_{n}}$$ (n = 0,1, . . .; $${u,\,x_0\in H}$$ given, and $${J_{\beta_n}=(I+\beta_nA)^{-1}}$$ , for a maximal monotone operator A) in a real Hilbert space, under new sets of conditions on $${\alpha_n\in(0,1)}$$ and $${\beta_n\in(0,\infty)}$$ . These conditions are weaker than those known to us and our results extend and improve some recent results such as those of H. K. Xu. We also show how to apply our results to approximate minimizers of convex functionals. In addition, we give convergence rate estimates for a sequence approximating the minimum value of such a functional.