On a class of multivalued variational inequalities. (1998)

• Record Type: Journal Article
• Authors: Noor, Muhammad Aslam
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 11:Number 1(1998)
• Page Start: 79
• Page End: 93
• Publication Date: 1998
• Subjects: variational inequalities -- fixed point problem -- Wiener- Hopf equations -- algorithms -- convergence criteria -- auxiliary principle -- optimization problems; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953398000070
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : In this paper, we introduce and study a new class of variational inequalities, which are called multivalued variational inequalities. These variational inequalities include as special cases, the previously known classes of variational inequalities. Using projection techniques, we show that multivalued variational inequalities are equivalent to fixed point problems and Wiener-Hopf equations. These alternate formulations are used to suggest a number of iterative algorithms for solving multivalued variational inequalities. We also consider the auxiliary principle technique to study the existence of a solution of multivalued variational inequalities and suggest a novel iterative algorithm. In addition, we have shown that the auxiliary principle technique can be used to find the equivalent differentiable optimization problems for multivalued variational inequalities. Convergence analysis is also discussed.