A gap function and existence of solutions for a non-smooth vector variational inequality on Hadamard manifolds. (2nd September 2021)

• Record Type: Journal Article
• Authors: Jayswal, Anurag; Kumari, Babli; Ahmad, Izhar
• Is Part Of: Optimization. Volume 70:Number 9(2021)
• Page Start: 1875
• Page End: 1889
• Publication Date: 2021-09-02
• Subjects: Mixed weak vector variational inequality -- gap function -- generalized monotone -- KKM mapping -- Hadamard manifold; 58E35 -- 47H05; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1759057
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In the present paper, a gap function for a non-smooth mixed weak vector variational inequality involving generalized gradient on Hadamard manifolds is obtained. A non-trivial example is presented to illustrate the relationship between a gap function and a non-smooth mixed weak vector variational inequality. The existence of solution for a non-smooth mixed weak vector variational inequality without monotonicity is also studied. Moreover, a g -pseudomonotone is introduced and it is employed to discuss the existence of solution for an aforesaid problem.