In a recent paper, Bauschke et al. study ρ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho...

This paper demonstrates a customized application of the classical proximal point algorithm (PPA) to the convex minimization problem with linear constraints. We show that if the proximal parameter in metric form is chosen appropriately, the application of PPA could be effective to exploit the...

This paper focuses on some customized applications of the proximal point algorithm (PPA) to two classes of problems: the convex minimization problem with linear constraints and a generic or separable objective function, and a saddle-point problem. We treat these two classes of problems uniformly...

In this paper, for a monotone operator T, we shall show strong convergence of the regularization method for Rockafellar’s proximal point algorithm under more relaxed conditions on the sequences {r <Subscript> k </Subscript>} and {t <Subscript> k </Subscript>}, <Equation ID="Equa"> <EquationSource Format="TEX">$$\lim\limits_{k\to\infty}t_k=0;\quad...</equationsource></equation></subscript></subscript>

In this paper we present an extension of the proximal point algorithm with Bregman distances to solve constrained minimization problems with quasiconvex and convex objective function on Hadamard manifolds. The proposed algorithm is a modified and extended version of the one presented in Papa...

The purpose of this paper is to show that the iterative scheme recently studied by Xu (J Glob Optim 36(1):115–125, <CitationRef CitationID="CR8">2006</CitationRef>) is the same as the one studied by Kamimura and Takahashi (J Approx Theory 106(2):226–240, <CitationRef CitationID="CR2">2000</CitationRef>) and to give a supplement to these results. With the new technique proposed...</citationref></citationref>

In this paper we consider the contraction-proximal point algorithm: <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${x_{n+1}=\alpha_nu+\lambda_nx_n+\gamma_nJ_{\beta_n}x_n,}$$< /EquationSource> </InlineEquation> where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${J_{\beta_n}}$$</EquationSource> </InlineEquation> denotes the resolvent of a monotone operator A. Under the assumption that lim<Subscript> n </Subscript> α <Subscript> n </Subscript> = 0, ∑<Subscript> n </Subscript> α <Subscript> n </Subscript> = ∞, lim inf<Subscript> n </Subscript> β <Subscript> n...</subscript></subscript></subscript></subscript></subscript></subscript></equationsource></inlineequation></equationsource></inlineequation>