Open AccessA study on vector variational-like inequalities using convexificators and application to its bi-level form
Author(s) -
Gayatri Pany,
R. N. Mohapatra
Publication year - 2022
Publication title -
journal of industrial and management optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.325
H-Index - 32
eISSN - 1553-166X
pISSN - 1547-5816
DOI - 10.3934/jimo.2021161
Subject(s) - variational inequality , mathematics , connection (principal bundle) , mathematical optimization , vector optimization , computer science , optimization problem , algebra over a field , pure mathematics , geometry , multi swarm optimization
This paper deals with the weak versions of the vector variational-like inequalities, namely Stampacchia and Minty type under invexity in the framework of convexificators. The connection between both the problems along with the link to vector optimization problem are analyzed. An application to nonconvex mathematical programming has also been presented. Further, the bi-level version of these problems is formulated and a procedure to obtain the solution involving the auxiliary principle technique is described in detail. We have shown that the iterative algorithm with the help of which we get the approximate solution converges strongly to the exact solution of the problem.