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We consider a general linear parabolic problem with extended time boundary conditions (including initial value problems and periodic ones), and approximate it by the implicit Euler scheme in time and the Gradient Discretisation method in…
In this paper, we propose new algorithms for finding a common point of the solution set of a pseudomonotone equilibrium problem and the set of fixed points of a symmetric generalized hybrid mapping in a real Hilbert space. The convergence…
We develop a weak adversarial approach to solving obstacle problems using neural networks. By employing (generalised) regularised gap functions and their properties we rewrite the obstacle problem (which is an elliptic variational…
A simple bilevel variational problem where the lower level is a variational inequality while the upper level is an optimization problem is studied. We consider an inexact version of the lower problem, which guarantees enough regularity to…
Learning processes are useful methodologies able to improve knowledge of real phenomena. These are often dependent on hyperparameters, variables set before the training process and regulating the learning procedure. Hyperparameters…
In this paper, we introduce three new iterative methods for finding a common point of the set of fixed points of a symmetric generalized hybrid mapping and the set of solutions of an equilibrium problem in a real Hilbert space. Each method…
This paper is concerned with the numerical minimization of energy functionals in Hilbert spaces involving convex constraints coinciding with a semi-norm for a subspace. The optimization is realized by alternating minimizations of the…
The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is…
In practice, optimization tasks have some structure that allows developing new algorithms for every problem with faster convergence rates. Using the structure of optimization tasks, we can propose algorithms with more optimistic convergence…
We obtain a general concept of triplet of Hilbert spaces with closed (unbounded) embeddings instead of continuous (bounded) ones. The construction starts with a positive selfadjoint operator $H$, that is called the Hamiltonian of the…
Solving equilibrium problems under constraints is an important problem in optimization and optimal control. In this context an important practical challenge is the efficient incorporation of constraints. We develop a continuous-time method…
We provide new complexity information for the convergence of the Hybrid Steepest Descent Method for solving the Variational Inequality Problem for a strict contraction on Hilbert space over a closed convex set C given either as the fixed…
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…
We consider a class of inexact Newton regularization methods for solving nonlinear inverse problems in Hilbert scales. Under certain conditions we obtain the order optimal convergence rate result.
We design and analyze a novel accelerated gradient-based algorithm for a class of bilevel optimization problems. These problems have various applications arising from machine learning and image processing, where optimal solutions of the two…
An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…
This paper studies the behavior of the extragradient algorithm [Korpelevich, 1976] when applied to hypomonotone operators, a class of problems that extends beyond the classical monotone setting. To support the understanding of this…
We propose a prototypical Split Inverse Problem (SIP) and a new variational problem, called the Split Variational Inequality Problem (SVIP), which is a SIP. It entails finding a solution of one inverse problem (e.g., a Variational…
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…
In this paper, we introduce a split general quasi-variational inequality problem which is a natural extension of split variational inequality problem, quasi-variational and variational inequality problems in Hilbert spaces. Using projection…