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pro vyhledávání: '"65k15"'
In this paper, we derive a three-operator splitting scheme for solving monotone inclusion and convex optimization problems from the three-block ADMM method on the dual problem. The proposed scheme can be regarded as an extension of the Douglas-Rachfo
Externí odkaz:
http://arxiv.org/abs/2411.00166
In this paper, we derive a priori error estimates for variational inequalities of the first kind in an abstract framework. This is done by combining the first Strang Lemma and the Falk Theorem. The main application consists in the derivation of a pri
Externí odkaz:
http://arxiv.org/abs/2410.22052
Autor:
Boţ, Radu Ioan, Chenchene, Enis
In this paper, we introduce a novel Extra-Gradient method with anchor term governed by general parameters. Our method is derived from an explicit discretization of a Tikhonov-regularized monotone flow in Hilbert space, which provides a theoretical fo
Externí odkaz:
http://arxiv.org/abs/2410.14369
The aim of this paper is to study the weak convergence analysis of sequence of iterates generated by a three-operator splitting method of Davis and Yin incorporated with two-step inertial extrapolation for solving monotone inclusion problem involving
Externí odkaz:
http://arxiv.org/abs/2410.01099
A popular method to perform adversarial attacks on neuronal networks is the so-called fast gradient sign method and its iterative variant. In this paper, we interpret this method as an explicit Euler discretization of a differential inclusion, where
Externí odkaz:
http://arxiv.org/abs/2406.05376
Autor:
Bot, Radu Ioan, Nguyen, Dang-Khoa
In the framework of real Hilbert spaces, we investigate first-order dynamical systems governed by monotone and continuous operators. We demonstrate that when the monotone operator flow is augmented with a Tikhonov regularization term, the resulting t
Externí odkaz:
http://arxiv.org/abs/2406.00852
Given a proper convex lower semicontinuous function defined on a Hilbert space and whose solution set is supposed nonempty. For attaining a global minimizer when this convex function is continuously differentiable, we approach it by a first-order con
Externí odkaz:
http://arxiv.org/abs/2404.00038
Autor:
Gfrerer, H., Outrata, J. V.
For the numerical solution of nonsmooth problems, sometimes it is not necessary that an exact subgradient/generalized Jacobian is at our disposal, but that a certain semismoothness property is fulfilled. In this paper we consider not only semismoothn
Externí odkaz:
http://arxiv.org/abs/2405.14637
The unique solvability and error analysis of the original Lagrange multiplier approach proposed in [8] for gradient flows is studied in this paper. We identify a necessary and sufficient condition that must be satisfied for the nonlinear algebraic eq
Externí odkaz:
http://arxiv.org/abs/2405.03415
In this work, we consider a nonsmooth minimisation problem in which the objective function can be represented as the maximum of finitely many smooth ``subfunctions''. First, we study a smooth min-max reformulation of the problem. Due to this smoothne
Externí odkaz:
http://arxiv.org/abs/2404.10326