Solving variational inequalities and cone complementarity problems in nonsmooth dynamics using the alternating direction method of multipliers
Sign Up to like & getrecommendations! Published in 2021 at "International Journal for Numerical Methods in Engineering"
DOI: 10.1002/nme.6693
Abstract: This work presents a numerical method for the solution of variational inequalities arising in nonsmooth flexible multibody problems that involve set‐valued forces. For the special case of hard frictional contacts, the method solves a second… read more here.
Keywords: direction method; alternating direction; cone complementarity; method ... See more keywords
Iterative method with inertial for variational inequalities in Hilbert spaces
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DOI: 10.1007/s10092-018-0300-5
Abstract: Strong convergence property for Halpern-type iterative method with inertial terms for solving variational inequalities in real Hilbert spaces is investigated under mild assumptions in this paper. Our proposed method requires only one projection onto the… read more here.
Keywords: inertial variational; iterative method; hilbert spaces; method ... See more keywords
A class of Benders decomposition methods for variational inequalities
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DOI: 10.1007/s10589-019-00157-y
Abstract: We develop new variants of Benders decomposition methods for variational inequality problems. The construction is done by applying the general class of Dantzig–Wolfe decomposition of Luna et al. (Math Program 143(1–2):177–209, 2014) to an appropriately… read more here.
Keywords: class; variational inequalities; methods variational; decomposition methods ... See more keywords
L∞-Error Analysis for Parabolic Quasi-Variational Inequalities Related to Impulse Control Problems
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DOI: 10.1007/s10598-016-9349-7
Abstract: This paper deals with the numerical analysis of the problem of parabolic quasi-variational inequalities related to impulse control problems. An optimal L∞-convergence of a piecewise linear finite element method is established using the concept of… read more here.
Keywords: impulse control; quasi variational; parabolic quasi; variational inequalities ... See more keywords
Expected Residual Minimization Formulation for a Class of Stochastic Vector Variational Inequalities
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DOI: 10.1007/s10957-016-0939-5
Abstract: This paper considers a class of vector variational inequalities. First, we present an equivalent formulation, which is a scalar variational inequality, for the deterministic vector variational inequality. Then we concentrate on the stochastic circumstance. By… read more here.
Keywords: expected residual; vector variational; residual minimization; variational inequalities ... See more keywords
A Class of Delay Differential Variational Inequalities
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DOI: 10.1007/s10957-016-1002-2
Abstract: In the paper, we introduce a class of delay differential variational inequalities consisting of a system of delay differential equations and variational inequalities. The existence conclusion of Carathéodory’s weak solution for delay differential variational equalities… read more here.
Keywords: differential variational; variational inequalities; class delay; delay differential ... See more keywords
Regularized Nonconvex Mixed Variational Inequalities: Auxiliary Principle Technique and Iterative Methods
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DOI: 10.1007/s10957-016-1046-3
Abstract: In this paper, we turn our attention to formulating and studying a new class of variational inequalities in a nonconvex setting, called regularized nonconvex mixed variational inequalities. By using the auxiliary principle technique, some new… read more here.
Keywords: principle technique; regularized nonconvex; auxiliary principle; variational inequalities ... See more keywords
On the Weak Convergence of the Extragradient Method for Solving Pseudo-Monotone Variational Inequalities
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DOI: 10.1007/s10957-017-1214-0
Abstract: In infinite-dimensional Hilbert spaces, we prove that the iterative sequence generated by the extragradient method for solving pseudo-monotone variational inequalities converges weakly to a solution. A class of pseudo-monotone variational inequalities is considered to illustrate… read more here.
Keywords: pseudo monotone; method solving; extragradient method; variational inequalities ... See more keywords
A New Double-Projection Method for Solving Variational Inequalities in Banach Spaces
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DOI: 10.1007/s10957-018-1228-2
Abstract: In this paper, we study the variational inequalities involving monotone and Lipschitz continuous mapping in Banach spaces. A new and simple iterative method, which combines Halpern’s technique and the subgradient extragradient idea, is given. Under… read more here.
Keywords: banach spaces; spaces new; method; variational inequalities ... See more keywords
Inertial Projection-Type Methods for Solving Quasi-Variational Inequalities in Real Hilbert Spaces
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DOI: 10.1007/s10957-019-01616-6
Abstract: In this paper, we introduce an inertial projection-type method with different updating strategies for solving quasi-variational inequalities with strongly monotone and Lipschitz continuous operators in real Hilbert spaces. Under standard assumptions, we establish different strong… read more here.
Keywords: real hilbert; quasi variational; solving quasi; variational inequalities ... See more keywords
The Global Exponential Stability of a Dynamical System for Solving Variational Inequalities
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DOI: 10.1007/s11067-019-09457-6
Abstract: We revisit a dynamical system for solving variational inequalities. Under strongly pseudomonotone and Lipschitz continuous assumptions of the considered operator, we obtain the global exponential stability of the trajectories. Numerical examples are presented confirming the… read more here.
Keywords: variational inequalities; dynamical system; stability; system solving ... See more keywords