We propose and study the iteration-complexity of an inexact version of the Spingarn’s partial inverse method. Its complexity analysis is performed by viewing it in the framework of the hybrid proximal extragradient (HPE) method, for which pointwise and ergodic iteration-complexity has been established recently by Monteiro and Svaiter. As applications, we propose and analyze the iteration-comple...

We propose a class of regularized Hermitian and skew-Hermitian splitting methods for the solution of large, sparse linear systems in saddle-point form. These methods can be used as stationary iterative solvers or as preconditioners for Krylov subspacemethods.We establish unconditional convergence of the stationary iterations and we examine the spectral properties of the corresponding preconditi...

In this paper we consider the contraction-proximal point algorithm: xn+1 = αnu+λnxn+γnJβnxn, where Jβn denotes the resolvent of a monotone operator A. Under the assumption that limn αn = 0, ∑ n αn = ∞, lim infn βn > 0, and lim infn γn > 0, we prove the strong convergence of the iterates as well as its inexact version. As a result we improve and recover some recent results by Boikanyo and Morosa...

This paper presents and studies the iteration-complexity of two new inexact variants of Rockafellar’s proximal method of multipliers (PMM) for solving convex programming (CP) problems with a finite number of functional inequality constraints. In contrast to the first variant which solves convex quadratic programming (QP) subproblems at every iteration, the second one solves convex constrained q...

In Rough Set Theory, dependency in the knowledge base is an important aspect when drawing inferences about the world. Rough set (inexact set) is defined by using a fixed binary relation (equivalence relation, tolerance relation, similarity relation, etc) to analyze vague, imprecise, inexact problems, which satisfy many interesting properties. The neighborhood based rough set theory is an extens...

We present an inexact interior point proximal method to solve linearly constrained convex problems. In fact, we derive a primal-dual algorithm to solve the KKT conditions of the optimization problem using a modified version of the rescaled proximal method. We also present a pure primal method. The proposed proximal method has as distinctive feature the possibility of allowing inexact inner step...

A new method is introduced for large scale convex constrained optimization. The general model algorithm involves, at each iteration, the approximate minimization of a convex quadratic on the feasible set of the original problem and global convergence is obtained by means of nonmonotone line searches. A specific algorithm, the Inexact Spectral Projected Gradient method (ISPG), is implemented usi...

In this paper, we extend the implementable APG method to solve the matrix l2,1-norm minimization problem arising in multi-task feature learning. We investigate that the resulting inner subproblem has closed-form solution which can be easily determined by taking the problem’s favorable structures. Under suitable conditions, we can establish a comprehensive convergence result for the proposed met...

Grabner basis is olle of the most important tools ill recent symbolic algebraic computations. Howe\'er, computing a Grobncr basis fo r the given polynomial ideal is lIot easy and it is lIot numcric.. . l1y stable if polynomials have inexact coefficients. I n this paper, we study what we should get for computing a Grabner basis with inexact coefficients alld introduce a naive method to compute a...

We analyze inexact fixed point iterations where the generating function contains an inexact solve of an equation system to answer the question of how tolerances for the inner solves influence the iteration error of the outer fixed point iteration. Important applications are the Picard iteration and partitioned fluid structure interaction. We prove that the iteration converges irrespective of ho...