In this paper, we provide two inertial projection methods with a
novel nonmonotonic adaptive step size for solving variational
inequalities governed by quasimonotone and Lipschitz continuous
operators in real Hilbert spaces. Compared with the general
subgradient extragradient method, our algorithms use a different
half-space. Under some suitable conditions, we obtain the weak
convergence theorem of the first modified inertial projection
algorithm and the strong convergence theorem of the second modified
viscosity-type inertial projection algorithm. Moreover, several
numerical results are given to illustrate the effectiveness and
competitiveness of our proposed methods.
