Related papers: Strong convergence of three-step iterative process…
In this paper, using generalized metric projection, we propose a new extragradient method for finding a common element of the solutions set of a generalized equilibrium problem and a variational inequality for an $\alpha$-inverse-strongly…
The purpose of this paper is to study an implicit scheme for a representation of nonexpansive mappings on a closed convex subset of a smooth and uniformly convex Banach space with respect to a left regular sequence of means defined on an…
Strong convergence of a new iterative process based on the Shrinking projection method to a common element of the set of common fixed points of an infinite family of relatively quasi-nonexpansive multivalued mappings and the solution set of…
The techniques of data-driven backmapping from coarse-grained (CG) to fine-grained (FG) representation often struggle with accuracy, unstable training, and physical realism, especially when applied to complex systems such as proteins. In…
This paper investigates the convergence of the randomized Kaczmarz algorithm for the problem of phase retrieval of complex-valued objects. While this algorithm has been studied for the real-valued case}, its generalization to the…
We study the generic behavior of the method of successive approximations for set-valued mappings in separable Banach spaces. We consider the case of nonexpansive mappings with convex and compact point images and show that for the typical…
Cellwise outliers are likely to occur together with casewise outliers in modern data sets with relatively large dimension. Recent work has shown that traditional robust regression methods may fail for data sets in this paradigm. The…
This paper deals with a general form of variational problems in Banach spaces which encompasses variational inequalities as well as minimization problems. We prove a characterization of local error bounds for the distance to the…
In this paper, using the monotone iterative technique and the Banach contraction mapping principle, we study a class of fractional differential system with integral boundary on an infinite interval. Some explicit monotone iterative schemes…
We establish strong duality relations for functional two-step compositional risk-constrained learning problems with multiple nonconvex loss functions and/or learning constraints, regardless of nonconvexity and under a minimal set of…
This work deals with the Mann's stochastic iteration algorithm under strong mixing random errors. We establish the Fuk-Nagaev's inequalities that enable us to prove the almost complete convergence with its corresponding rate of convergence.…
In this paper, we present some common fixed point theorems for a commuting pair of mappings, including a generalized nonexpansive single valued mapping and a generalized nonexpansive multivalued mapping in strictly convex Banach spaces. The…
We introduce a new extragradient iterative process, motivated and inspired by [S. H. Khan, A Picard-Mann Hybrid Iterative Process, Fixed Point Theory and Applications, doi:10.1186/1687-1812-2013-69], for finding a common element of the set…
It has been proposed that classical filtering methods, like the Kalman filter and 3DVAR, can be used to solve linear statistical inverse problems. In the work of Iglesias, Lin, Lu, & Stuart (2017), error estimates were obtained for this…
We consider a class of inverse problems defined by a nonlinear map from parameter or model functions to the data. We assume that solutions exist. The space of model functions is a Banach space which is smooth and uniformly convex; however,…
We study a class of monotone inclusions called "self-concordant inclusion" which covers three fundamental convex optimization formulations as special cases. We develop a new generalized Newton-type framework to solve this inclusion. Our…
In this short note, we formulate the convergence rates of the well known Tikhonov regularization scheme for solving the nonlinear ill-posed problems in Banach spaces. For deriving the convergence rates, we employ the novel smoothness…
The article deals with gradient-like iterative methods for solving nonlinear operator equations on Hilbert and Banach spaces. The authors formulate a general principle of studying such methods. This principle allows to formulate simple…
Deep learning algorithms have been applied very successfully in recent years to a range of problems out of reach for classical solution paradigms. Nevertheless, there is no completely rigorous mathematical error and convergence analysis…
Many recently introduced enhanced sampling techniques are based on biasing coarse descriptors (collective variables) of a molecular system on the fly. Sometimes the calculation of such collective variables is expensive and becomes a…