Related papers: Beyond Monotone Variational Inequalities: Solution…
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…
Extremal problems are studied involving an objective function with values in (order) complete lattices of sets generated by so called set relations. Contrary to the popular paradigm in vector optimization, the solution concept for such…
This paper establishes the convergence properties of the Popov mirror-prox algorithm for solving stochastic and deterministic variational inequalities (VIs) under a polynomial growth condition on the mapping variation. Unlike existing…
Basing on some recently proposed methods for solving variational inequalities with non-smooth operators, we propose an analogue of the Mirror Prox method for the corresponding class of problems under the assumption of relative smoothness…
Variational inequalities (VIs) are a broad class of optimization problems encompassing machine learning problems ranging from standard convex minimization to more complex scenarios like min-max optimization and computing the equilibria of…
This paper presents a modified iterative approach to solve the variational inequality problem using the double inertial technique in the context of a real Hilbert space. Our iterative technique involves a projection onto a generalized…
Circumcentered techniques have been shown to significantly accelerate projection-based methods for convex feasibility problems. Motivated by this success, we propose two direct methods with circumcenter acceleration for solving variational…
Inspired by the adaptive Golden Ratio Algorithm (aGRAAL), we propose two new methods for solving monotone variational inequalities. We show that by selecting the momentum parameter beyond the golden ratio in aGRAAL, the convergence speed…
We propose a study of structured non-convex non-concave min-max problems which goes beyond standard first-order approaches. Inspired by the tight understanding established in recent works [Adil et al., 2022, Lin and Jordan, 2022b], we…
This paper explores a new class of constrained difference programming problems, where the objective and constraints are formulated as differences of functions, without requiring their convexity. To investigate such problems, novel variants…
In this paper, we introduce a new method for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. The iterative process is based on two well-known projection method and the hybrid (or…
The article is devoted to some adaptive methods for variational inequalities with relatively smooth and relatively strongly monotone operators. Starting from the recently proposed proximal variant of the extragradient method for this class…
This paper deals with quasi-variational inequality problems (QVIs) in a generic Banach space setting. We provide a theoretical framework for the analysis of such problems which is based on two key properties: the pseudomonotonicity (in the…
Solutions of a variational inequality are found by giving conditions for the monotone convergence with respect to a cone of the Picard iteration corresponding to its natural map. One of these conditions is the isotonicity of the projection…
In this paper, we develop stochastic variance reduced algorithms for solving a class of finite-sum hemivariational inequality (HVI) problem. In this HVI problem, the associated function is assumed to be differentiable, and both the vector…
This survey on stationary and evolutionary problems with gradient constraints is based on developments of monotonicity and compactness methods applied to large classes of scalar and vectorial solutions to variational and quasi-variational…
This paper establishes comprehensive stability results for quasi-variational inequalities (QVIs) under monotone perturbations of the governing operator. We prove strong convergence of both minimal and maximal solutions when sequences of…
Variational inequalities are a universal optimization paradigm that is interesting in itself, but also incorporates classical minimization and saddle point problems. Modern realities encourage to consider stochastic formulations of…
An interesting observation is that most pairs of weakly homogeneous mappings have no strongly monotonic property, which is one of the key conditions to ensure the unique solvability of the generalized variational inequality. This paper…
We investigate a structured class of nonconvex-nonconcave min-max problems exhibiting so-called \emph{weak Minty} solutions, a notion which was only recently introduced, but is able to simultaneously capture different generalizations of…