Related papers: Termination criteria for inexact fixed point metho…
We show that the effects of finite-precision arithmetic in forming and solving the linear system that arises at each iteration of primal-dual interior-point algorithms for nonlinear programming are benign, provided that the iterates satisfy…
This paper is concerned with the study of a family of fixed point iterations combining relaxation with different inertial (acceleration) principles. We provide a systematic, unified and insightful analysis of the hypotheses that ensure…
This paper is devoted to first-order algorithms for smooth convex optimization with inexact gradients. Unlike the majority of the literature on this topic, we consider the setting of relative rather than absolute inexactness. More…
Recent empirical studies have identified fixed point iteration phenomena in deep neural networks, where the hidden state tends to stabilize after several layers, showing minimal change in subsequent layers. This observation has spurred the…
We study the convergence of an inexact version of the classical Krasnosel'skii-Mann iteration for computing fixed points of nonexpansive maps. Our main result establishes a new metric bound for the fixed-point residuals, from which we…
Recent efforts on solving inverse problems in imaging via deep neural networks use architectures inspired by a fixed number of iterations of an optimization method. The number of iterations is typically quite small due to difficulties in…
Let $C$ be a closed cone with nonempty interior $C^\circ$ in a Banach space. Let $f:C^\circ \rightarrow C^\circ$ be an order-preserving subhomogeneous function with a fixed point in $C^\circ$. We introduce a condition which guarantees that…
Floating-point arithmetic performance determines the overall performance of important applications, from graphics to AI. Meeting the IEEE-754 specification for floating-point requires that final results of addition, subtraction,…
We point out how Banach Fixed Point Theorem, and the Picard successive approximation methods induced by it, allows us to treat some mathematical methods in Combinatorics. In particular we get, by this way, a proof and an iterative algorithm…
This note considers the inexact cubic-regularized Newton's method (CR), which has been shown in \cite{Cartis2011a} to achieve the same order-level convergence rate to a secondary stationary point as the exact CR \citep{Nesterov2006}.…
We prove a general finite convergence theorem for "upward-guarded" fixpoint expressions over a well-quasi-ordered set. This has immediate applications in regular model checking of well-structured systems, where a main issue is the eventual…
In this paper, we present error estimates of the integral deferred correction method constructed with stiffly accurate implicit Runge-Kutta methods with a nonsingular matrix $A$ in its Butcher table representation, when applied to stiff…
In this paper, we present an inexact Noda iteration with inner-outer iterations for finding the smallest eigenvalue and the associated eigenvector of an irreducible monotone matrix. The proposed inexact Noda iteration contains two main…
We present a class of iterative fully distributed fixed point methods to solve a system of linear equations, such that each agent in the network holds one of the equations of the system. Under a generic directed, strongly connected network,…
In a recent paper~\cite{paper2}, we proposed the concept of optimal error bounds for an iterative process, which allows us to obtain the convergence result of the iterative sequence to the common fixed point of the nonexpansive mappings in…
We apply methods of the fixed point theory to a Lambda policy iteration with a randomization algorithm for weak contractions mappings. This type of mappings covers a broader range than the strong contractions typically considered in the…
In this article we investigate an inexact iterative regularization method based on generalized Bregman distances of an optimal control problem with control constraints. We show robustness and convergence of the inexact Bregman method under…
We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…
We study iterative finite element approximations for the numerical approximation of semilinear elliptic boundary value problems with monotone nonlinear reactions of subcritical growth. The focus of our contribution is on an optimal a priori…
This paper proposes a fully distributed termination method for distributed optimization algorithms solved by multiple agents. The proposed method guarantees terminating a distributed optimization algorithm after satisfying the global…