In this paper we propose two different primal-dual splitting algorithms for solving inclusions involving mixtures of composite and parallel-sum type monotone operators which rely on an inexact Douglas-Rachford splitting method, however applied in different underlying Hilbert spaces. Most importantly, the algorithms allow to process the bounded linear operators and the set-valued operators occur...

The purpose of this paper is to introduce an implicit iterative process with errors for approximating common fixed point of two finite families of asymptotically nonexpansive mappings in the framework of Banach space. The results presented in this paper extend and generalize the corresponding results of Qin et al.[Convergence analysis of implicit iterative algorithms for asymptotically nonexpan...

We define an algebraic framework based on non-safe Petri nets, which allows one to express operations such as iteration, parallel composition, and transition synchronisation. This leads to an algebra of process expressions, whose constants and operators directly correspond to those used in Petri nets, and so we are able to associate nets to process expressions compositionally. The semantics of ...

A new method is presented for the reconstruction of the radiocarbon production rate from the measured relative abundance of ∆14C. The method treats the carbon cycle as a linear Fourier filter and thus allows for the correct and unambiguous inversion of the carbon cycle. The 14C production rate, as reconstructed by the Fourier filter method, agrees with the results obtained by the traditional it...

The k-support-norm regularized minimization has recently been applied with success to sparse prediction problems. The proximal gradient method is conventionally used to minimize this composite model. However it tends to suffer from expensive iteration cost thus the model solving could be time consuming. In our work, we reformulate the k-support-norm regularized formulation into a constrained fo...

In this paper, we apply the Newton’s and He’s iteration formulas in order to solve the nonlinear algebraic equations. In this case, we use the stochastic arithmetic and the CESTAC method to validate the results. We show that the He’s iteration formula is more reliable than the Newton’s iteration formula by using the CADNA library.

We propose new stochastic gradient algorithms for solving convex composite optimization problems. In each iteration, our algorithms utilize a stochastic oracle of the gradient of the smooth component in the objective function. Our algorithms are based on a stochastic version of the estimate sequence technique introduced by Nesterov (Introductory Lectures on Convex Optimization: A Basic Course, ...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 16 January 2020Accepted: 09 July 2021Published online: 25 October 2021Keywordsquadratic penalty method, composite nonconvex problem, iteration complexity, inexact proximal point first-order accelerated gradient minimax problemAMS Subject Headings47J22, 90C26, 90C30, 90C47...

‎The ABS methods‎, ‎introduced by Abaffy‎, ‎Broyden and Spedicato‎, ‎are‎‎direct iteration methods for solving a linear system where the‎‎$i$-th iteration satisfies the first $i$ equations‎, ‎therefore a‎ ‎system of $m$ equations is solved in at most $m$ steps‎. ‎In this‎‎paper‎, ‎we introduce a class of ABS-type methods for solving a full row‎‎rank linear equations‎, ‎w...

this paper presents a comparison between variational iteration method (vim) and modfied variational iteration method (mvim) for approximate solution a system of volterra integral equation of the first kind. we convert a system of volterra integral equations to a system of volterra integro-di®erential equations that use vim and mvim to approximate solution of this system and hence obtain an appr...