Existence And Sensitivity Analysis Of Solutions For Two Classess Of Generalized System Of Variational Inclusions

It is well known that variational inequality theory is very powerful tools of the current mathematical technology. Variational inequalities have many important applications in operation research, computer science, system science, engineering technology, transportation, economics and management et.al. In the last 20 years of the twentith century, they have been paid close attention by many scholars. They become an important foundation and tool for studying multiobjective and multilevel programs and one of focal point problems paid close attention by scholars in the field of applied mathematics, research on which touch upon such mathematical branches as convex, linear analysis and nonlinear analysis, nonsmooth analysis, set-valued analysis. Generalized variational inclusions are generalization of variational inequalities, they have wide applications in fields of optimization and control, economics and transportation equilibrium, engineering science. Some scholars considered the traffic equilibrium problem, the spatial equilibrium problem, the Nash equilibrium, and the general equilibrium programming problem can be modeled as a problem of variational inequalities. Therefore, the research for them has important learning value.In this paper, we introduce several kinds of generalized variational inequalities and system of variational inclusions, study the existence of the solutions and the sensitivity of the parametric solutions systematically, construct some iterative algorithms for solving the system of generalized nonlinear mixed quasi-variational inclusions, the convergence of the iterative sequence generated by the algorithms proposed are also given. The results generalize, unify and extend a large number of known results related to variational inequalities, variatioal inclusions, and the system of variatioal inequalities. Details are as follows.(1) In chapter 2, we use three-step projection methods to consider a generalized system for relaxed cocoercive variational inequalities with error estimate in Hilbert space. We use the implicit resolvent operator and fixed point therom to prove the approximation solvability and convergence.(2) In chapter 3, we introduce and study a system of nonlinear set-valued implicit variational inclusions (SNSIVI) with relaxed cocoercive mappings in real Banach spaces. By using resolvent operator technique for .H-accretive operators, we construct a new class of perturbed iterative algorithms for solving this system of set-valued implicit variational inclusions. We also prove the convergence of the iterative algorithms in q-uniformly smooth Banach spaces.(3) In chapter 4, we use the implicit resolvent equations technique to study the sensitivity analysis for the generalized multi-valued quasi-variational inclusions.(4) In chapter 5, we introduce a new system of generalized nonlinear parametric mixed quasi-variational inclusions, prove the existence of solution, and give the sensitivity analysis of solution in Hilbert spaces.