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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…

Numerical Analysis · Mathematics 2014-10-09 Zhenying Zhang , Eduard Bader , Karen Veroy

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…

Optimization and Control · Mathematics 2025-11-20 Xiaozhi Liu , Yong Xia

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…

Optimization and Control · Mathematics 2015-12-31 J. Y. Bello Cruz , R. Diaz Millan

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…

Optimization and Control · Mathematics 2025-05-12 Gourav Kumar , Santanu Soe , V. Vetrivel

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…

Optimization and Control · Mathematics 2022-12-21 Shaolin Tan , Jinhu Lu

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…

Optimization and Control · Mathematics 2021-05-05 Jeffrey Cornelis , Wim Vanroose

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…

Optimization and Control · Mathematics 2023-12-08 Zeinab Alizadeh , Felipe Parra Polanco , Afrooz Jalilzadeh

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…

Numerical Analysis · Mathematics 2024-12-16 Bosu Choi , Jihun Han , Yoonsang Lee

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…

Optimization and Control · Mathematics 2024-09-26 Quoc Tran-Dinh , Nghia Nguyen-Trung

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…

Optimization and Control · Mathematics 2012-10-05 Kazufumi Ito , Tomoya Takeuchi

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…

Robotics · Computer Science 2019-07-03 Benoit Landry , Zachary Manchester , Marco Pavone

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…

Machine Learning · Computer Science 2018-02-02 Linbo Qiao , Tianyi Lin , Qi Qin , Xicheng Lu

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…

Functional Analysis · Mathematics 2014-08-19 Kaleem Raza Kazmi

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…

Numerical Analysis · Mathematics 2016-02-04 Martin Benning , Carola-Bibiane Schönlieb , Tuomo Valkonen , Verner Vlačić

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…

Optimization and Control · Mathematics 2025-05-16 Mohammad Khalafi , Digvijay Boob

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…

Optimization and Control · Mathematics 2021-06-16 Prashant Khanduri , Siliang Zeng , Mingyi Hong , Hoi-To Wai , Zhaoran Wang , Zhuoran Yang

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…

Optimization and Control · Mathematics 2024-09-13 Abhishek Chakraborty , Angelia Nedić

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…

Optimization and Control · Mathematics 2023-09-06 Monica Bianchi , Enrico Miglierina , Maede Ramazannejad

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…

Optimization and Control · Mathematics 2026-01-22 Sudkobfa Boontawee , Mootta Prangprakhon , Nimit Nimana

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…

Machine Learning · Computer Science 2019-05-15 Kumar Shridhar , Felix Laumann , Marcus Liwicki