Abstract
In this paper, we present two new inertial projection-type methods for solving multivalued variational inequality problems in finite-dimensional spaces. We establish the convergence of the sequence generated by these methods when the multivalued mapping associated with the problem is only required to be locally bounded without any monotonicity assumption. Furthermore, the inertial techniques that we employ in this paper are quite different from the ones used in most papers. Moreover, based on the weaker assumptions on the inertial factor in our methods, we derive several special cases of our methods. Finally, we present some experimental results to illustrate the profits that we gain by introducing the inertial extrapolation steps.
Highlights
Assume that C is a nonempty closed and convex subset of RN and F : C ⇒ RN a multivalued mapping with nonempty values
Problem (MVIP) associated with F and C consists in finding x∗ ∈ C and u ∈ F (x∗) such that u, y − x∗ ≥ 0, ∀y ∈ C
As observed in He et al (2019, Section 4), Algorithm 1.1, Algorithm 1.2 and Algorithm 1.3 do not work well in some settings because of the presence of Procedure A in the iterative steps. The authors in He et al (2019) proposed the following projection-type method without Procedure A for solving MVIP (1), which can be implemented in such settings
Summary
Assume that C is a nonempty closed and convex subset of RN and F : C ⇒ RN a multivalued mapping with nonempty values. The authors in He et al (2019) proposed the following projection-type method without Procedure A for solving MVIP (1), which can be implemented in such settings. We present two inertial projection-type methods for solving MVIP (1) when the multivalued mapping F is only assumed to be locally bounded without any monotonicity assumption.
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