This article proposes a new algorithm for solving a class of composite convex-concave saddlepoint problems. The new algorithm is a special instance of the hybrid proximal extragradient framework in which a Nesterov’s accelerated variant is used to approximately solve the prox subproblems. One of the advantages of the new method is that it works for any constant choice of proximal stepsize. More...

This paper presents a proximal point approach for computing the Riemannian or intrinsic Karcher mean of, n×n, symmetric positive definite (SPD) matrices. Our method derives from proximal point algorithm with Schur decomposition developed to compute minimum points of convex functions on SPD matrices set when it is seen as a Hadamard manifold. The main idea of the original method is preserved. Ho...

We propose a Newton-CG primal proximal point algorithm for solving large scale log-determinant optimization problems. Our algorithm employs the essential ideas of the proximal point algorithm, the Newton method and the preconditioned conjugate gradient solver. When applying the Newton method to solve the inner sub-problem, we find that the log-determinant term plays the role of a smoothing term...

In this paper, we present a measure of distance in second-order cone based on a class of continuously differentiable strictly convex function on IR++. Since the distance function has some favorable properties similar to those of D-function [8], we here refer it as a quasi D-function. Then, a proximal-like algorithm using the quasi D-function is proposed and applied to the second-cone programmin...

In this paper we study and compare the notions of uniform convexity of functions at a point and on bounded sets with the notions of total convexity at a point and sequential consistency of functions, respectively. We establish connections between these concepts of strict convexity in infinite dimensional settings and use the connections in order to obtain improved convergence results concerning...

In this work, we propose and study a framework of generalized proximal point algorithms associated with maximally monotone operator. We indicate sufficient conditions on the regularization relaxation parameters for equivalence boundedness sequence iterations generated by algorithm non-emptiness zero set operator, weak strong convergence algorithm. Our results cover or improve many in our refere...

Conditions are given for the viability and the weak convergence of an inexact, relaxed proximal point algorithm for finding a common zero of countably many cohypomonotone operators in a Hilbert space. In turn, new convergence results are obtained for an extended version of the proximal method of multipliers in nonlinear programming.

In this paper, we investigate the proximal split feasibility algorithm and fixed point problem in Hilbert spaces. We propose an iterative for finding a common element of solution L-Lipschitz pseudocontractive operator. demonstrate that considered converges strongly to investigated problems under some mild conditions.