变分不等式和相补问题及其对经济与金融的应用

In this projection, we studied some kinds of generalized variational inequalities and complementarity problems, generalized.variational inclusion problems, implicit vector equilibrium problems and vector variational inequality problems, and the problems of fixed points and coupled fixed points for set-valued mappings with applications. We constructed some algorithms for proximating the solutions of the problems, proved the convergence of the algorithms, and obtained some new results. The study of the variational-like inequality problems involving the.generalized monotone mappings in Banach spaces is considered as quite interesting by the referee. We introduced the new concepts of exceptional family of elements and utilized these notions to the study of the feasibility of the nonlinear zomplementarity problems in the.finite-dimensional and nfinite-dimensional spaces, which answered one of the three open problems proposed by the Canadian mathematician G. Isac in 2000. The referee said, “this paper can be considered as an interesting contribution to the mprovement of the topological methods based on the.notion of EFE”.

本项目研究拟似变分不等式、半变分不等式、变分不等式和相补系统、变分包含、向量变分不等式和补问题解的存在性，解集的有界性，灵敏性分析，逼近解的算法，算法的收敛性与稳定性，广义非线性动力系统均衡问题，经济与金融均衡问题及期权定价问题。本项目的研究对非线性分析与动力系统理论和算法以及国民经济的发展将起到积极的推动作用。