Abstract
The purpose of this work to investigate pseudomonotone and Lipschitz continuous variational inequalities in real Hilbert spaces. For solving this problem, we propose two new methods which combine advantages of the subgradient extragradient method and the projection contraction method. Similar to some recent developments, the proposed methods do not require the knowledge of the Lipschitz constant associated with the variational inequality mapping. Under suitable mild conditions, we establish the weak and strong convergence of the proposed algorithms. Moreover, linear convergence is obtained under strong pseudomonotonicity and Lipschitz continuity assumptions. Numerical examples in fractional programming and optimal control problems demonstrate the potential of our algorithms as well as compare their performances to several related results.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
