Combined Relaxation Methods for Variational Inequalities

By Igor V. Konnov. 2000

597 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/09ae336bbd9149ae05aa89284478d21466896568

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In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Convergence Analysis of Modified Hybrid Steepest-Descent Methods with Variable Parameters for Variational Inequalities (2007, unknown): “Let the sequence {un} be generated by algorithm (7).”
Modified Tseng's extragradient methods for solving pseudo-monotone variational inequalities (2019, methodology): “Solution methods solving the variational inequality (1) have been developed extensively in the literature [4, 5, 6, 10, 16, 17, 18, 19, 23, 24, 28, 30, 31, 33, 34].”
Using the Banach Contraction Principle to Implement the Proximal Point Method for Multivalued Monotone Variational Inequalities (2005, unknown): “Then, from (10), (11), and ( 12 ), it follows that”
Extragradient algorithms extended to equilibrium problems (2008, methodology): “The linesearch technique has been used widely in descent methods for mathematical programing problems as well as for variational inequalities [9,13].”
Common Solutions to Variational Inequalities (2012, background): “For an excellent treatise on variational inequality problems in nite-dimensional spaces, see the two-volume book by Facchinei and Pang [12].”
Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence (2020, background): “Several applications of VI(A,C) (1) are discussed in [2, 4, 18, 25, 26, 27, 32].”
Single projection method for pseudo-monotone variational inequality in Hilbert spaces (2018, background): “Therefore, the knowledge of fixed-point algorithms (see, for example, [6,8,9]) can be used to solve VI(A,C) (1).”
Mann-Type Steepest-Descent and Modified Hybrid Steepest-Descent Methods for Variational Inequalities in Banach Spaces (2008, unknown): “, see, for example, [6, 8, 10, 17, 21, 22, 30, 41, 42] and references therein.”
An efficient iterative method for finding common fixed point and variational inequalities in Hilbert spaces (2018, methodology): “The VI is investigated intensively and there exists many iterative methods for solving it and other related optimization problems, for example see the monographs [8,10] and references therein.”
A projection algorithm for solving pseudomonotone equilibrium problems and it's application to a class of bilevel equilibria (2013, background): “The proof of this lemma when f is pseudomonotone on C can be found, for instance, in [2,22].”
Parallel Extragradient-Proximal Methods for Split Equilibrium Problems (2015, methodology): “Almost proposed methods for SEPs based on the proximal method [18] w hich consists of solving a regularized equilibrium problem, i.”
Advances in Variational and Hemivariational Inequalities (2015, methodology): “We recall that hemivariational inequalities, introduced and studied in the early 1980s by Panagiotopoulos in [19, 20], are closely related to nonlinear inclusions of subdifferential type.”
Application of the Proximal Point Method to Nonmonotone Equilibrium Problems (2003, methodology): “At the same time, Basic Scheme 1 still works due to Theorem 31, and we can apply the same Lagrangian duality approach to the auxiliary EP ( 12 ).”