A Generalized Proximal Point Algorithm and Its Convergence Rate

2014 ◽  
Vol 24 (4) ◽  
pp. 1614-1638 ◽  
Author(s):  
Etienne Corman ◽  
Xiaoming Yuan
Keyword(s):  
Convergence Rate ◽  
Proximal Point Algorithm ◽  
Proximal Point ◽  
Generalized Proximal Point Algorithm

scholarly journals Convergence of a Proximal Point Algorithm for Solving Minimization Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Abdelouahed Hamdi ◽  
M. A. Noor ◽  
A. A. Mukheimer
Keyword(s):  
Convergence Rate ◽  
Proximal Point Algorithm ◽  
Iterative Scheme ◽  
Point Method ◽  
Proximal Point Method ◽  
Proximal Point ◽  
Minimization Problems ◽  
Estimate Rate ◽  
Proximal Term ◽  
Better Than

We introduce and consider a proximal point algorithm for solving minimization problems using the technique of Güler. This proximal point algorithm is obtained by substituting the usual quadratic proximal term by a class of convex nonquadratic distance-like functions. It can be seen as an extragradient iterative scheme. We prove the convergence rate of this new proximal point method under mild assumptions. Furthermore, it is shown that this estimate rate is better than the available ones.

scholarly journals ON THE CONVERGENCE RATE OF THE KRASNOSEL’SKIĬ–MANN ITERATION

2017 ◽  
Vol 96 (1) ◽  
pp. 162-170 ◽  
Author(s):  
SHIN-YA MATSUSHITA
Keyword(s):  
Fixed Point ◽  
Convergence Rate ◽  
Proximal Point Algorithm ◽  
Convergence Rates ◽  
Fixed Point Problems ◽  
Proximal Point ◽  
Mann Iteration

The Krasnosel’skiĭ–Mann (KM) iteration is a widely used method to solve fixed point problems. This paper investigates the convergence rate for the KM iteration. We first establish a new convergence rate for the KM iteration which improves the known big-$O$ rate to little-$o$ without any other restrictions. The proof relies on the connection between the KM iteration and a useful technique on the convergence rate of summable sequences. Then we apply the result to give new results on convergence rates for the proximal point algorithm and the Douglas–Rachford method.

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