In this paper, the proximal point algorithm for quasi-convex minimization problem in nonpositive curvature metric spaces is studied. We prove ∆-convergence of the generated sequence to a critical point (which is defined in the text) of an objective convex, proper and lower semicontinuous function with at least a minimum point as well as some strong convergence results to a minimum point with so...

We propose a Projected Proximal Point Algorithm (ProPPA) for solving a class of optimization problems. The algorithm iteratively computes the proximal point of the last estimated solution projected into an affine space which itself is parallel and approaching to the feasible set. We provide convergence analysis theoretically supporting the general algorithm, and then apply it for solving `1-min...

In this article, we introduce a new notion of proximal contraction, named as generalized S-proximal contraction and derive a common best proximity point theorem for proximally commuting non-self mappings, thereby yielding the common optimal approximate solution of some fixed point equations when there is no common solution. We furnish illustrative examples to highlight our results. We extend so...

The purpose of this paper is to provide some remarks for the main results of the paper Verma (Appl. Math. Lett. 21:142-147, 2008). Further, by using the generalized proximal operator technique associated with the (A,η,m)-monotone operators, we discuss the approximation solvability of general variational inclusion problem forms in Hilbert spaces and the convergence analysis of iterative sequence...

This paper recalls the proximal point method. We study two iterative algorithms: the Blahut-Arimoto algorithm for computing the capacity of arbitrary discrete memoryless channels, as an example of an iterative algorithm working with probability density estimates and the iterative decoding of the Bit Interleaved Coded Modulation (BICM-ID). For these iterative algorithms, we apply the proximal po...

In this study, we introduce a primal-dual prediction-correction algorithm framework for convex optimization problems with known saddle-point structure. Our unified frame adds the proximal term with a positive definite weighting matrix. Moreover, different proximal parameters in the frame can derive some existing well-known algorithms and yield a class of new primal-dual schemes. We prove the co...

In this paper we extend naturally the scalarization proximal point method to solve multiobjective unconstrained minimization problems, proposed by Apolinario et al.[1], from Euclidean spaces to Hadamard manifolds for locally Lipschitz and quasiconvex vector objective functions. Moreover, we present a convergence analysis, under some mild assumptions on the multiobjective function, for two inexa...

Ha 7] recently introduced the generalized proximal point algorithm for solving the generalized equation. In this note, we present the generalized proximal point algorithm for convex optimization problems based on Ha's work. The idea behind this algorithm is that instead of adding a quadratic term to all the variables, we add a quadratic term to a subset of the variables. We extend the criteria ...