Algorithm Research On Several Classes Of Mixed Variational Inequality

Variational inequality theory is developed accompanying the study of nonlinear problems in continuous mechanics in1960’s, which is a very powerful tool of the current mathematical technology. Variational inequalities have many important applications in differential equations, elasticity, physics, economics, control theory, optimization theory and so on. Mixed variational inequalities are effective generalization of variational inequalities, which play a prominent role in optimization theory and economics. This thesis mainly studies several classes of mixed variational inequalities on the aspects of algorithm.First, the auxiliary variational principle is applied to solve a class of variational inequality in Hilbert spaces. The iterative algorithm to compute approximate solution is constructed and the convergence of iterative sequences generated by the algorithm is proved.Second, a class of bilinear variational inequality in Banach spaces is studied. By KKM theory, the existence result of solutions of the auxiliary problem with respect to the variational inequality is shown. An iterative algorithm is established and the convergence of iterative sequences generated by the algorithm is proved.Third, a class of generalized set-valued mixed variational inequality with fuzzy mapping in Hilbert spaces is discussed. Using resolvent operator principle, the equivalence is established between the variational inequality and the resolvent equation. An iterative algorithm is established and the convergence of iterative sequences is proved.