相关论文: An inertial iteratively regularized extragradient …

Motivated by problems in contact mechanics, we propose a duality approach for computing approximations and associated a posteriori error bounds to solutions of variational inequalities of the first kind. The proposed approach improves upon…

The Extragradient (EG) method stands as a cornerstone algorithm for solving monotone nonlinear equations but faces two important unresolved challenges: (i) how to select stepsizes without relying on the global Lipschitz constant or…

We introduce a relaxed-projection splitting algorithm for solving variational inequalities in Hilbert spaces for the sum of nonsmooth maximal monotone operators, where the feasible set is defined by a nonlinear and nonsmooth continuous…

This article analyses the simple projection method proposed by Izuchukwu et al. [8, Algorithm 3.2] for solving variational inequality problems by incorporating momentum terms. A new step size strategy is also introduced, in which the step…

In this technical note, we are concerned with the problem of solving variational inequalities with improved convergence rates. Motivated by Nesterov's accelerated gradient method for convex optimization, we propose a Nesterov's accelerated…

Interior-point methods for linear programming problems require the repeated solution of a linear system of equations. Solving these linear systems is non-trivial due to the severe ill-conditioning of the matrices towards convergence. This…

We consider a stochastic Inverse Variational Inequality (IVI) problem defined by a continuous and co-coercive map over a closed and convex set. Motivated by the absence of performance guarantees for stochastic IVI, we present a…

Regularization is a critical technique for ensuring well-posedness in solving inverse problems with incomplete measurement data. Traditionally, the regularization term is designed based on prior knowledge of the unknown signal's…

This paper presents a comprehensive analysis of the well-known extragradient (EG) method for solving both equations and inclusions. First, we unify and generalize EG for [non]linear equations to a wider class of algorithms, encompassing…

We propose an implicit iterative algorithm for an exact penalty method arising from inequality constrained optimization problems. A rapidly convergent fixed point method is developed for a regularized penalty functional. The applicability…

Many problems in modern robotics can be addressed by modeling them as bilevel optimization problems. In this work, we leverage augmented Lagrangian methods and recent advances in automatic differentiation to develop a general-purpose…

In this paper, we propose a stochastic Primal-Dual Hybrid Gradient (PDHG) approach for solving a wide spectrum of regularized stochastic minimization problems, where the regularization term is composite with a linear function. It has been…

In this paper, we introduce a system of split variational inequality problems in real Hilbert spaces. Using projection method, we propose an iterative algorithm for the system of split variational inequality problems. Further, we prove that…

We explore anisotropic regularisation methods in the spirit of [Holler & Kunisch, 14]. Based on ground truth data, we propose a bilevel optimisation strategy to compute the optimal regularisation parameters of such a model for the…

The bilevel variational inequality (BVI) problem is a general model that captures various optimization problems, including VI-constrained optimization and equilibrium problems with equilibrium constraints (EPECs). This paper introduces a…

This paper proposes a new algorithm -- the \underline{S}ingle-timescale Do\underline{u}ble-momentum \underline{St}ochastic \underline{A}pprox\underline{i}matio\underline{n} (SUSTAIN) -- for tackling stochastic unconstrained bilevel…

This paper considers a variational inequality (VI) problem arising from a game among multiple agents, where each agent aims to minimize its own cost function subject to its constrained set represented as the intersection of a (possibly…

In a normed space setting, this paper studies the conditions under which the projected solutions to a quasi equilibrium problem with non-self constraint map exist. Our approach is based on an iterative algorithm which gives rise to a…

In this letter, we consider a bilevel optimization problem in which the outer-level objective function is strongly convex, whereas the inner-level problem consists of a finite sum of convex functions. Bilevel optimization problems arise in…

We introduce a novel uncertainty estimation for classification tasks for Bayesian convolutional neural networks with variational inference. By normalizing the output of a Softplus function in the final layer, we estimate aleatoric and…