3,857 research outputs found
A von Neumann Alternating Method for Finding Common Solutions to Variational Inequalities
Modifying von Neumann's alternating projections algorithm, we obtain an
alternating method for solving the recently introduced Common Solutions to
Variational Inequalities Problem (CSVIP). For simplicity, we mainly confine our
attention to the two-set CSVIP, which entails finding common solutions to two
unrelated variational inequalities in Hilbert space.Comment: Nonlinear Analysis Series A: Theory, Methods & Applications, accepted
for publicatio
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
- …