Abstract
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+βnA)-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 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.
Original language | English |
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Pages (from-to) | 11-26 |
Number of pages | 16 |
Journal | Journal of Global Optimization |
Volume | 51 |
Issue number | 1 |
DOIs | |
Publication status | Published - Sept 2011 |
All Science Journal Classification (ASJC) codes
- Control and Optimization
- Applied Mathematics
- Computer Science Applications
- Management Science and Operations Research