A new modified subgradient extragradient method for solving variational inequalities

Abstract

The goal of the note is to introduce a new modified subgradient extragradient algorithm for solving variational inequalities in Hilbert spaces. A result on the strong convergence of the algorithm is proved without the knowledge of Lipschitz constant of the operator. Several numerical experiments for the proposed algorithm are presented.

COMMUNICATED BY:

• Dumitru Motreanu

Keywords:

• Subgradient extragradient algorithm
• strong convergence
• Lipschitz continuity
• variational inequality
• projection

2010 Mathematics Subject Classifications:

• 47J20
• 90C25
• 90C30
• 90C52

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This project is supported by the H2020-MSCA-RISE-2018 Research and Innovation Staff Exchange Scheme Fellowship within the Project No. 823731 CONMECH, National Science Center of Poland under Maestro Project No. UMO-2012/06/A/ST1/00262, National Science Center of Poland under Preludium Project No. 2017/25/N/ST1/00611. It is also supported by the International Project co-financed by the Ministry of Science and Higher Education of Republic of Poland under Grant No. 3792/GGPJ/H2020/2017/0, National Natural Science Foundation of China (Grant Nos. 11561007 and 11561008), Natural Sciences Foundation of Guangxi (Grant No. 2018JJA110006), Beibu Gulf University Project No. 2018KYQD06. The second author is also supported by the National Natural Science Foundation of China (No. 11771350), Basic and Advanced Research Project of CQ CSTC (Nos. cstc2016jcyjA0163 and cstc2018jcyjAX0605).