A variant of korpelevich’s method for variational inequalities with a new search strategy

By Alfredo Noel Iusem, Benar Fux Svaiter. 1997

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In Mathematical Optimization

Citations in the corpus

Projected Reflected Gradient Methods for Monotone Variational Inequalities (2015, methodology): “The extragradient method has received a great deal of attention by many authors, who improved it in various ways; see, e.g., [4,7,9,17] and references therein.”
A modified Korpelevich's method convergent to the minimum-norm solution of a variational inequality (2014, methodology): “Moreover, we would like to cite the idea introduced by Iusem in [10] for the finite-dimensional case and developed in [12] by Iusem and Svaiter and in [1,2] by Bello Cruz and Iusem in more general setting of the Hilbert space or for the paramonotone variational inequality.”
The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space (2011, background): “, [3,4,5] and references therein, to name but a few.”
New extragradient method for a class of equilibrium problems in Hilbert spaces (2018, result): “We have the following corollary which should be shared with the results in [24,28,37,38].”
Strong convergence of subgradient extragradient methods for the variational inequality problem in Hilbert space (2011, background): “, [16, 17, 23] and references therein, to name but a few.”
Extensions of Korpelevich's extragradient method for the variational inequality problem in Euclidean space (2012, methodology): “In general, projection algorithms that use metric projections onto the set S require that f be Lipschitz continuous, meaning that there exists an L 0 such that k f ðxÞ f ð yÞk Lkx yk, ð1:4Þ and strongly monotone, meaning that there exists an 0 such that f ðxÞ f ð yÞ, x y kx yk2. ð1:5Þ By adding the ”
Strong convergence of a double projection-type method for monotone variational inequalities in Hilbert spaces (2018, methodology): “The extragradient method was further extended to infinite-dimensional spaces by many authors; see, for instance, [1, 10, 12, 18, 20, 21, 35, 38, 40].”
A Strongly Convergent Direct Method for Monotone Variational Inequalities in Hilbert Spaces (2009, methodology): “When T is not Lipschitz, or it is Lipschitz but the constant L is not known, the fixed stepsize in the first step must be replaced by a stepsize computed through an Armijo-type search, as in the following method, present in [10].”