Problems Of Existence And Approximation Of Solutions For The Variational Inequalities

In this dissertation, two problems in the variational inequality theory are mainly considered: the existence of solutions and the approximation schemes. We obtain some new results.First, we mainly study a class of generalized set-valued vector variational inequality problem (GVVIP). We extend the generalized L-condition and the generalized v-coercive condition (C₂) in reference [7] to the set-valued circumstance. Then we establish serveal existence results and apply them in the generalized vector complementarity problem (GVCP)_T. Secondly, we study a class of generalized multivalued variational inequality and transform it to the variational inclusion problem. By using resolvent operator techniques, we obtain the equivalence between variational inequality problem and the fixed point problem, so we establish the three-step iterative algorithm of approximation solution. lastly, we discuss the application of inf-convolution and ε—subdifferential to the minimum problems and obtain the description of the ε—subdifferential of the distance function.