Algorithms for General Mixed Quasi Variational Inequalities

Volume 3, Issue 4, 2002

Article 59

ALGORITHMS FOR GENERAL MIXED QUASI VARIATIONAL INEQUALITIES

MUHAMMAD ASLAM NOOR AND ZULFIQAR ALI MEMON

ETISALAT COLLEGE OF ENGINEERING
SHARJAH, UNITED ARAB EMIRATES.
E-Mail: noor@ece.ac.ae

E-Mail: ali@ece.ac.ae

Received 1 May, 2002; Accepted 12 May, 2002.
Communicated by: Th.M. Rassias

ABSTRACT. In this paper, we use the auxiliary principle technique to suggest and analyze a predictor-corrector method for solving general mixed quasi variational inequalities. If the bifunction involving the mixed quasi variational inequalities is skew-symmetric , then it is shown that the convergence of the new method requires the partially relaxed strongly monotonicity of the operator, which is a weaker condition than cocoercivity. Since the general mixed quasi variational inequalities includes the classical quasi variational inequalities and complementarity problems as special cases, results obtained in this paper continue to hold for these problems. Our results can be viewed an important extension of the previously known results for variational inequalities.

Key words:
Variational inequalities, Auxiliary principle, Predictor-corrector method, Resolvent operator, Convergence.

2000 Mathematics Subject Classification:
49J40, 90C33.

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