A new projection-type method for solving multi-valued mixed variational inequalities without monotonicity

ABSTRACT

In this paper, a new projection-type algorithm for solving multi-valued mixed variational inequalities without monotonicity is presented. Under some suitable assumptions, it is showed that the sequence generated by the proposed algorithm converges globally to a solution of the multi-valued mixed variational inequality considered. The algorithm exploited in this paper is based on the generalized f -projection operator due to Wu and Huang [The generalized f-projection operator with an application. Bull Austral Math Soc. 2006;73:307–317] rather than the well-known resolvent operator. Preliminary computational experience is also reported. The results presented in this paper generalize and improve some known results given in the literature.

Keywords:

• Multi-valued mixed variational inequalities
• generalized f -projection operators
• projection-type method

2010 MSC:

• 49J53
• 58E35

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [11701479, 11526170, 11701478, 11771067, 11526169, 11601450] and the Fundamental Research Funds for the Central Universities [2682017CX062].