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.
"Convergence of a Proximal Point Algorithm for Solving Minimization Problems." J. Appl. Math. 2012 (SI03) 1 - 13, 2012. https://doi.org/10.1155/2012/142862