Modified resolvent algorithm for general mixed quasi-variational inequalities

Authors:
M. A. Noor
Affiliations:
Etisalat College of Engineering Sharjah, United Arab Emirates
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2002

Citing 3
Cited 2

Some aspects of variational inequalities

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Predictor-corrector iterative algorithms for solving generalized mixed quasi-variational-like inclusion

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Predictor-corrector iterative algorithms for solving generalized mixed quasi-variational-like inclusion

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Abstract

It is well known [1] that the general mixed quasi-variational inequalities are equivalent to the implicit resolvent equations. In this paper, we use this alternative formulation to suggest and analyze a modified resolvent algorithm for solving general mixed quasi-variational inequalities. It is shown that the convergence of the new modified method only requires the pseudomonotonicity, which is a weaker condition than monotonicity. Since the general mixed quasi-variational inequalities include the general (mixed) variational inequalities and related optimization problems as special cases, results obtained in this paper continue to hold for these problems. Our results can be viewed as significant extensions of previously known results including those of Noor [1-3] and Solodov and Tseng [4] for various classes of variational inequalities.