集值均衡问题统一了集值优化、变分不等式和互补等数学问题, 在投资决策、最优控制和工程技术等领域有广泛的应用. 由于所包含问题的广泛性和统一性以及解决问题的深刻性, 均衡问题成为当今运筹学与非线性分析研究领域中的一个热点问题. .本项目将提出集值均衡问题的若干近似解，研究近似解与原解之间的关系，在非凸假设下，讨论近似解的非线性标量化. 讨论近似解的非导数型最优性条件..借助逼近锥族针对集值均衡问题提出一类新的内逼近解. 讨论逼近解和原解之间的关系, 在近似锥-次类凸假设下, 研究标量化定理, 讨论逼近解的对偶问题. 研究逼近解对参数的灵敏度分析及参数扰动后对解的影响. 我们拟研究的内逼近解问题也属变序结构的均衡问题. . 本项目的研究尤其是关于变序结构均衡问题的研究不仅可以丰富均衡理论，也可推动相关学科的发展, 且具有重要的潜在应用价值.

Set-valued equilibrium problem unifies set-valued optimization, variational inequality and complementarity, and has a wide range of applications in investment decision-making, optimal control and engineering technology. Due to the universality and unity of the problems involved and the profundity of solving them, equilibrium problem has become a hot issue in the field of operational research and non-linear analysis..Several kinds of outer approximate solutions to the equilibrium problem with set-valued maps will be introduced. The relationship between outer approximate solutions and original solutions will be discussed. Without the assumption of convexity, the nonlinear scalarization problem on outer approximate solutions will be considered. Non-derivative optimality conditions will be established..With the help of approximation families of a cone, a new kind of inner approximate solutions will be introduced for the equilibrium problem with set-valued maps. The relationship between inner approximate solutions and original solutions will be discussed. Under the assumption of near cone-subconvexlikeness for set-valued maps, the scalarization theorems will be obtained. Also, inner approximate duality assertions will be established for inner approximate solutions. The behavior of the perturbation map will be analyzed quantitatively and the influence of parameter perturbation on solutions will be discussed. The inner approximation problem we are going to study is also an equilibrium problem with variable structure..This research, especially on the equilibrium problem of variable structure, not only enriches the equilibrium theory, but also promotes the development of related disciplines, and has important potential application value.