相关论文: Convergence analysis for pseudo-monotone variation…
In this work we consider an iterative method for solving the quasi-convex feasibility problem. We firstly introduce the so-called star subgradient projection operator and present some useful properties. We subsequently obtain a convergence…
The 2-sets convex feasibility problem aims at finding a point in the nonempty intersection of two closed convex sets $A$ and $B$ in a Hilbert space $X$. The method of alternating projections is the simplest iterative procedure for finding a…
In this paper, we propose a new method that combines the inexact Newton method with a procedure to obtain a feasible inexact projection for solving constrained smooth and nonsmooth equations. The local convergence theorems are established…
A new adaptive approach is proposed for variational inequalities with a Lipschitz-continuous field. Estimates of the necessary number of iterations are obtained to achieve a given quality of the variational inequality solution. A…
This paper is intended to solve the nonconvex $\ell_{p}$-ball constrained nonlinear optimization problems. An iteratively reweighted method is proposed, which solves a sequence of weighted $\ell_{1}$-ball projection subproblems. At each…
A numerical scheme is presented to solve the one source near field refractor problem to arbitrary precision and it is proved that the scheme terminates in a finite number of iterations. The convergence of the algorithm depends upon proving…
This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of infinite dimensional Hilbert spaces. For this purpose, several inertial hybrid and shrinking projection algorithms are proposed…
This paper deals with the convex feasibility problem, where the feasible set is given as the intersection of a (possibly infinite) number of closed convex sets. We assume that each set is specified algebraically as a convex inequality,…
We introduce a new system of split variational inequality problems which is a natural extension of split variational inequality problem in semi-inner product spaces. We use the retraction technique to propose an iterative algorithm for…
In this paper, we consider the inverse problem of determining the location and the shape of a sound-soft obstacle from the modulus of the far-field data for a single incident plane wave. By adding a reference ball artificially to the…
We propose and study the weak convergence of a projective splitting algorithm for solving multi-term composite monotone inclusion problems involving the finite sum of $n$ maximal monotone operators, each of which having an inner four-block…
It is well known that the projection method is not convergent for monotone equilibrium problems. Recently Sosa \textit{et al.} in \cite{SS2011} proposed a projection algorithm ensuring convergence for paramonotone equilibrium problems. In…
Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…
We consider constrained minimization problems and propose to replace the projection onto the entire feasible region, required in the Projected Subgradient Method (PSM), by projections onto the individual sets whose intersection forms the…
In this paper, we propose an algorithm combining the forward-backward splitting method and the alternative projection method for solving the system of splitting inclusion problem. We want to find a point in the interception of a finite…
A new class of projected dynamical systems of third order is investigated for quasi (parametric) variational inequalities in which the convex set in the classical variational inequality also depends upon the solution explicitly or…
For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…
In this paper we develop a stochastic heavy ball method for solving ill-posed inverse problems. The method updates the iterate using only a randomly selected equation at each iteration step while incorporating a momentum term into the…
The article is devoted to some adaptive methods for variational inequalities with relatively smooth and relatively strongly monotone operators. Starting from the recently proposed proximal variant of the extragradient method for this class…
We study some methods of subgradient projections for solving a convex feasibility problem with general (not necessarily hyperplanes or half-spaces) convex sets in the inconsistent case and propose a strategy that controls the relaxation…