1,424 research outputs found
An efficient projection-type method for monotone variational inequalities in Hilbert spaces
We consider the monotone variational inequality problem in a Hilbert space and describe a projection-type method with inertial terms under the following properties: (a) The method generates a strongly convergent iteration sequence; (b) The method requires, at each iteration, only one projection onto the feasible set and two evaluations of the operator; (c) The method is designed for variational inequality for which the underline operator is monotone and uniformly continuous; (d) The method includes an inertial term. The latter is also shown to speed up the convergence in our numerical results. A comparison with some related methods is given and indicates that the new method is promising
The Forward-Backward-Forward Method from continuous and discrete perspective for pseudo-monotone variational inequalities in Hilbert spaces
Tseng's forward-backward-forward algorithm is a valuable alternative for
Korpelevich's extragradient method when solving variational inequalities over a
convex and closed set governed by monotone and Lipschitz continuous operators,
as it requires in every step only one projection operation. However, it is
well-known that Korpelevich's method converges and can therefore be used also
for solving variational inequalities governed by pseudo-monotone and Lipschitz
continuous operators. In this paper, we first associate to a pseudo-monotone
variational inequality a forward-backward-forward dynamical system and carry
out an asymptotic analysis for the generated trajectories. The explicit time
discretization of this system results into Tseng's forward-backward-forward
algorithm with relaxation parameters, which we prove to converge also when it
is applied to pseudo-monotone variational inequalities. In addition, we show
that linear convergence is guaranteed under strong pseudo-monotonicity.
Numerical experiments are carried out for pseudo-monotone variational
inequalities over polyhedral sets and fractional programming problems
Weak convergence for variational inequalities with inertial-type method
Weak convergence of inertial iterative method for solving variational inequalities is the focus of this paper. The cost function is assumed to be non-Lipschitz and monotone. We propose a projection-type method with inertial terms and give weak convergence analysis under appropriate conditions. Some test results are performed and compared with relevant methods in the literature to show the efficiency and advantages given by our proposed methods
Inertial projection-type methods for solving quasi-variational inequalities in real Hilbert spaces
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 convergence results for the proposed algorithm. Primary numerical experiments demonstrate the potential applicability of our scheme compared with some related methods in the literature
Strong convergence of inertial extragradient algorithms for solving variational inequalities and fixed point problems
The paper investigates two inertial extragradient algorithms for seeking a
common solution to a variational inequality problem involving a monotone and
Lipschitz continuous mapping and a fixed point problem with a demicontractive
mapping in real Hilbert spaces. Our algorithms only need to calculate the
projection on the feasible set once in each iteration. Moreover, they can work
well without the prior information of the Lipschitz constant of the cost
operator and do not contain any line search process. The strong convergence of
the algorithms is established under suitable conditions. Some experiments are
presented to illustrate the numerical efficiency of the suggested algorithms
and compare them with some existing ones.Comment: 25 pages, 12 figure
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