相关论文: On compositions of special cases of Lipschitz cont…
Properties of compositions and convex combinations of averaged nonexpansive operators are investigated and applied to the design of new fixed point algorithms in Hilbert spaces. An extended version of the forward-backward splitting…
We study a conical extension of averaged nonexpansive operators and the role it plays in convergence analysis of fixed point algorithms. Various properties of conically averaged operators are systematically investigated, in particular, the…
Continuing the study initiated in our earlier article [7], this paper aims to characterize various continuity properties of nonlinear composition operators acting on some sequence spaces, giving special attention to the space of sequences…
Resolvent compositions were recently introduced as monotonicity-preserving operations that combine a set-valued monotone operator and a bounded linear operator. They generalize in particular the notion of a resolvent average. We analyze the…
We propose a method for solving constrained fixed point problems involving compositions of Lipschitz pseudo contractive and firmly nonexpansive operators in Hilbert spaces. Each iteration of the method uses separate evaluations of these…
The correspondence between the class of nonexpansive mappings and the class of maximally monotone operators via the reflected resolvents of the latter has played an instrumental role in the convergence analysis of the splitting methods.…
Fixed-point equations with Lipschitz operators have been studied for more than a century, and are central to problems in mathematical optimization, game theory, economics, and dynamical systems, among others. When the Lipschitz constant of…
The paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in…
The Douglas-Rachford method is a popular splitting technique for finding a zero of the sum of two subdifferential operators of proper closed convex functions; more generally two maximally monotone operators. Recent results concerned with…
We establish complete characterizations of various notions of expansivity for weighted composition operators on a very general class of locally convex spaces of continuous functions. This class includes several classical classes of…
We consider the problem of analyzing and designing gradient-based discrete-time optimization algorithms for a class of unconstrained optimization problems having strongly convex objective functions with Lipschitz continuous gradient. By…
While monotone operator theory is often studied on Hilbert spaces, many interesting problems in machine learning and optimization arise naturally in finite-dimensional vector spaces endowed with non-Euclidean norms, such as…
We study the weighted composition operators between the Lipschitz space and the space of bounded functions on the set of vertices of an infinite tree. We characterized the boundedness, the compactness, and the boundedness from below of…
In this paper we present an inexact zeroth-order method suitable for the solution nonsmooth and nonconvex stochastic composite optimization problems, in which the objective is split into a real-valued Lipschitz continuous stochastic…
This note studies numerical methods for solving compositional optimization problems, where the inner function is smooth, and the outer function is Lipschitz continuous, non-smooth, and non-convex but exhibits one of two special structures…
Nonexpansive mappings play a central role in modern optimization and monotone operator theory because their fixed points can describe solutions to optimization or critical point problems. It is known that when the mappings are sufficiently…
Proximal splitting algorithms for monotone inclusions (and convex optimization problems) in Hilbert spaces share the common feature to guarantee for the generated sequences in general weak convergence to a solution. In order to achieve…
In this article, we study the convergence of algorithms for solving monotone inclusions in the presence of adjoint mismatch. The adjoint mismatch arises when the adjoint of a linear operator is replaced by an approximation, due to…
The Lipschitz constant plays a crucial role in certifying the robustness of neural networks to input perturbations. Since calculating the exact Lipschitz constant is NP-hard, efforts have been made to obtain tight upper bounds on the…
In this note unbounded hyperexpansive weighted composition operators are investigated. AS a consequence unbounded hyperexpansive multiplication and composition operators are characterized.