The Experts below are selected from a list of 34632 Experts worldwide ranked by ideXlab platform
Leonid Prigozhin - One of the best experts on this subject based on the ideXlab platform.
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a quasi Variational Inequality problem arising in the modeling of growing sandpiles
arXiv: Analysis of PDEs, 2012Co-Authors: John W Barrett, Leonid PrigozhinAbstract:Existence of a solution to the quasi-Variational Inequality problem arising in a model for sand surface evolution has been an open problem for a long time. Another long-standing open problem concerns determining the dual variable, the flux of sand pouring down the evolving sand surface, which is also of practical interest in a variety of applications of this model. Previously, these problems were solved for the special case in which the Inequality is simply Variational. Here, we introduce a regularized mixed formulation involving both the primal (sand surface) and dual (sand flux) variables. We derive, analyse and compare two methods for the approximation, and numerical solution, of this mixed problem. We prove subsequence convergence of both approximations, as the mesh discretization parameters tend to zero; and hence prove existence of a solution to this mixed model and the associated regularized quasi-Variational Inequality problem. One of these numerical approximations, in which the flux is approximated by the divergence-conforming lowest order Raviart-Thomas element, leads to an efficient algorithm to compute not only the evolving pile surface, but also the flux of pouring sand. Results of our numerical experiments confirm the validity of the regularization employed.
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a quasi Variational Inequality problem in superconductivity
Mathematical Models and Methods in Applied Sciences, 2010Co-Authors: John W Barrett, Leonid PrigozhinAbstract:We derive a class of analytical solutions and a dual formulation of a scalar two-space-dimensional quasi-Variational Inequality problem in applied superconductivity. We approximate this formulation by a fully practical finite element method based on the lowest order Raviart–Thomas element, which yields approximations to both the primal and dual variables (the magnetic and electric fields). We prove the subsequence convergence of this approximation, and hence prove the existence of a solution to both the dual and primal formulations, for strictly star-shaped domains. The effectiveness of the approximation is illustrated by numerical examples with and without this domain restriction.
Houyuan Jiang - One of the best experts on this subject based on the ideXlab platform.
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Stochastic Approximation Approaches to the Stochastic Variational Inequality Problem
IEEE Transactions on Automatic Control, 2008Co-Authors: Houyuan JiangAbstract:Stochastic approximation methods have been extensively studied in the literature for solving systems of stochastic equations and stochastic optimization problems where function values and first order derivatives are not observable but can be approximated through simulation. In this paper, we investigate stochastic approximation methods for solving stochastic Variational Inequality problems (SVIP) where the underlying functions are the expected value of stochastic functions. Two types of methods are proposed: stochastic approximation methods based on projections and stochastic approximation methods based on reformulations of SVIP. Global convergence results of the proposed methods are obtained under appropriate conditions.
Amit Bhaya - One of the best experts on this subject based on the ideXlab platform.
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algorithm for Variational Inequality problems based on a gradient dynamical system designed using a control liapunov function
International Symposium on Intelligent Control, 2007Co-Authors: Fernando A Pazos, Amit BhayaAbstract:We present an algorithm to find the optimal point of a Variational Inequality problem. The domain of the function that defines the Variational Inequality is a convex set, determined by convex Inequality constraints and affine equality constraints. The algorithm is based on a discrete variable structure closed-loop control system which presents sliding mode trajectories on the boundary of the feasible set until the optimal point is reached. The update law is designed using control Liapunov function (CLF), which guarantees the decrease of a discrete Liapunov function inside and outside the feasible set. The step size is optimized using Liapunov optimizing control (LOC).
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ISIC - Algorithm for Variational Inequality problems based on a gradient dynamical system designed using a control Liapunov function
2007 IEEE 22nd International Symposium on Intelligent Control, 2007Co-Authors: Fernando A Pazos, Amit BhayaAbstract:We present an algorithm to find the optimal point of a Variational Inequality problem. The domain of the function that defines the Variational Inequality is a convex set, determined by convex Inequality constraints and affine equality constraints. The algorithm is based on a discrete variable structure closed-loop control system which presents sliding mode trajectories on the boundary of the feasible set until the optimal point is reached. The update law is designed using control Liapunov function (CLF), which guarantees the decrease of a discrete Liapunov function inside and outside the feasible set. The step size is optimized using Liapunov optimizing control (LOC).
John W Barrett - One of the best experts on this subject based on the ideXlab platform.
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a quasi Variational Inequality problem arising in the modeling of growing sandpiles
arXiv: Analysis of PDEs, 2012Co-Authors: John W Barrett, Leonid PrigozhinAbstract:Existence of a solution to the quasi-Variational Inequality problem arising in a model for sand surface evolution has been an open problem for a long time. Another long-standing open problem concerns determining the dual variable, the flux of sand pouring down the evolving sand surface, which is also of practical interest in a variety of applications of this model. Previously, these problems were solved for the special case in which the Inequality is simply Variational. Here, we introduce a regularized mixed formulation involving both the primal (sand surface) and dual (sand flux) variables. We derive, analyse and compare two methods for the approximation, and numerical solution, of this mixed problem. We prove subsequence convergence of both approximations, as the mesh discretization parameters tend to zero; and hence prove existence of a solution to this mixed model and the associated regularized quasi-Variational Inequality problem. One of these numerical approximations, in which the flux is approximated by the divergence-conforming lowest order Raviart-Thomas element, leads to an efficient algorithm to compute not only the evolving pile surface, but also the flux of pouring sand. Results of our numerical experiments confirm the validity of the regularization employed.
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a quasi Variational Inequality problem in superconductivity
Mathematical Models and Methods in Applied Sciences, 2010Co-Authors: John W Barrett, Leonid PrigozhinAbstract:We derive a class of analytical solutions and a dual formulation of a scalar two-space-dimensional quasi-Variational Inequality problem in applied superconductivity. We approximate this formulation by a fully practical finite element method based on the lowest order Raviart–Thomas element, which yields approximations to both the primal and dual variables (the magnetic and electric fields). We prove the subsequence convergence of this approximation, and hence prove the existence of a solution to both the dual and primal formulations, for strictly star-shaped domains. The effectiveness of the approximation is illustrated by numerical examples with and without this domain restriction.
Bingnan Jiang - One of the best experts on this subject based on the ideXlab platform.
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weak convergence theorem for a class of split Variational Inequality problems and applications in a hilbert space
Journal of Inequalities and Applications, 2017Co-Authors: Ming Tian, Bingnan JiangAbstract:In this paper, we consider the algorithm proposed in recent years by Censor, Gibali and Reich, which solves split Variational Inequality problem, and Korpelevich’s extragradient method, which solves Variational Inequality problems. As our main result, we propose an iterative method for finding an element to solve a class of split Variational Inequality problems under weaker conditions and get a weak convergence theorem. As applications, we obtain some new weak convergence theorems by using our weak convergence result to solve related problems in nonlinear analysis and optimization.
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weak convergence theorem for Variational Inequality problems with monotone mapping in hilbert space
Journal of Inequalities and Applications, 2016Co-Authors: Ming Tian, Bingnan JiangAbstract:We know that Variational Inequality problem is very important in the nonlinear analysis. The main purpose of this paper is to propose an iterative method for finding an element of the set of solutions of a Variational Inequality problem with a monotone and Lipschitz continuous mapping in Hilbert space. This iterative method is based on the extragradient method. We get a weak convergence theorem. Using this result, we obtain three weak convergence theorems for the equilibrium problem, the constrained convex minimization problem, and the split feasibility problem.
